MinT - Best Known (32, 41, s)-Nets in Base 256

Best Known (32, 41, s)-Nets in Base 256

(32, 41, large)-Net over F₂₅₆ — Constructive and digital

Digital (32, 41, large)-net over F₂₅₆, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 0, 32640)-net over F₂₅₆, using
  - s-reduction based on digital (0, 0, s)-net over F₂₅₆ with arbitrarily large s, using
    - arbitrary set of 256⁰ points [i]
2. digital (0, 0, 32640)-net over F₂₅₆ (see above)
3. digital (0, 0, 32640)-net over F₂₅₆ (see above)
4. digital (0, 0, 32640)-net over F₂₅₆ (see above)
5. digital (0, 0, 32640)-net over F₂₅₆ (see above)
6. digital (0, 0, 32640)-net over F₂₅₆ (see above)
7. digital (0, 0, 32640)-net over F₂₅₆ (see above)
8. digital (0, 0, 32640)-net over F₂₅₆ (see above)
9. digital (0, 0, 32640)-net over F₂₅₆ (see above)
10. digital (0, 0, 32640)-net over F₂₅₆ (see above)
11. digital (0, 0, 32640)-net over F₂₅₆ (see above)
12. digital (0, 0, 32640)-net over F₂₅₆ (see above)
13. digital (0, 0, 32640)-net over F₂₅₆ (see above)
14. digital (0, 0, 32640)-net over F₂₅₆ (see above)
15. digital (0, 0, 32640)-net over F₂₅₆ (see above)
16. digital (0, 0, 32640)-net over F₂₅₆ (see above)
17. digital (0, 0, 32640)-net over F₂₅₆ (see above)
18. digital (0, 0, 32640)-net over F₂₅₆ (see above)
19. digital (0, 0, 32640)-net over F₂₅₆ (see above)
20. digital (0, 0, 32640)-net over F₂₅₆ (see above)
21. digital (0, 0, 32640)-net over F₂₅₆ (see above)
22. digital (0, 0, 32640)-net over F₂₅₆ (see above)
23. digital (0, 0, 32640)-net over F₂₅₆ (see above)
24. digital (0, 0, 32640)-net over F₂₅₆ (see above)
25. digital (0, 0, 32640)-net over F₂₅₆ (see above)
26. digital (0, 0, 32640)-net over F₂₅₆ (see above)
27. digital (0, 0, 32640)-net over F₂₅₆ (see above)
28. digital (0, 0, 32640)-net over F₂₅₆ (see above)
29. digital (0, 0, 32640)-net over F₂₅₆ (see above)
30. digital (0, 0, 32640)-net over F₂₅₆ (see above)
31. digital (0, 0, 32640)-net over F₂₅₆ (see above)
32. digital (0, 0, 32640)-net over F₂₅₆ (see above)
33. digital (0, 0, 32640)-net over F₂₅₆ (see above)
34. digital (0, 0, 32640)-net over F₂₅₆ (see above)
35. digital (0, 0, 32640)-net over F₂₅₆ (see above)
36. digital (0, 0, 32640)-net over F₂₅₆ (see above)
37. digital (0, 0, 32640)-net over F₂₅₆ (see above)
38. digital (0, 0, 32640)-net over F₂₅₆ (see above)
39. digital (0, 0, 32640)-net over F₂₅₆ (see above)
40. digital (0, 0, 32640)-net over F₂₅₆ (see above)
41. digital (0, 0, 32640)-net over F₂₅₆ (see above)
42. digital (0, 0, 32640)-net over F₂₅₆ (see above)
43. digital (0, 0, 32640)-net over F₂₅₆ (see above)
44. digital (0, 0, 32640)-net over F₂₅₆ (see above)
45. digital (0, 0, 32640)-net over F₂₅₆ (see above)
46. digital (0, 0, 32640)-net over F₂₅₆ (see above)
47. digital (0, 0, 32640)-net over F₂₅₆ (see above)
48. digital (0, 0, 32640)-net over F₂₅₆ (see above)
49. digital (0, 0, 32640)-net over F₂₅₆ (see above)
50. digital (0, 0, 32640)-net over F₂₅₆ (see above)
51. digital (0, 0, 32640)-net over F₂₅₆ (see above)
52. digital (0, 0, 32640)-net over F₂₅₆ (see above)
53. digital (0, 0, 32640)-net over F₂₅₆ (see above)
54. digital (0, 0, 32640)-net over F₂₅₆ (see above)
55. digital (0, 0, 32640)-net over F₂₅₆ (see above)
56. digital (0, 0, 32640)-net over F₂₅₆ (see above)
57. digital (0, 0, 32640)-net over F₂₅₆ (see above)
58. digital (0, 0, 32640)-net over F₂₅₆ (see above)
59. digital (0, 0, 32640)-net over F₂₅₆ (see above)
60. digital (0, 0, 32640)-net over F₂₅₆ (see above)
61. digital (0, 0, 32640)-net over F₂₅₆ (see above)
62. digital (0, 0, 32640)-net over F₂₅₆ (see above)
63. digital (0, 0, 32640)-net over F₂₅₆ (see above)
64. digital (0, 0, 32640)-net over F₂₅₆ (see above)
65. digital (0, 0, 32640)-net over F₂₅₆ (see above)
66. digital (0, 0, 32640)-net over F₂₅₆ (see above)
67. digital (0, 0, 32640)-net over F₂₅₆ (see above)
68. digital (0, 0, 32640)-net over F₂₅₆ (see above)
69. digital (0, 0, 32640)-net over F₂₅₆ (see above)
70. digital (0, 0, 32640)-net over F₂₅₆ (see above)
71. digital (0, 0, 32640)-net over F₂₅₆ (see above)
72. digital (0, 0, 32640)-net over F₂₅₆ (see above)
73. digital (0, 0, 32640)-net over F₂₅₆ (see above)
74. digital (0, 0, 32640)-net over F₂₅₆ (see above)
75. digital (0, 0, 32640)-net over F₂₅₆ (see above)
76. digital (0, 0, 32640)-net over F₂₅₆ (see above)
77. digital (0, 0, 32640)-net over F₂₅₆ (see above)
78. digital (0, 0, 32640)-net over F₂₅₆ (see above)
79. digital (0, 0, 32640)-net over F₂₅₆ (see above)
80. digital (0, 0, 32640)-net over F₂₅₆ (see above)
81. digital (0, 0, 32640)-net over F₂₅₆ (see above)
82. digital (0, 0, 32640)-net over F₂₅₆ (see above)
83. digital (0, 0, 32640)-net over F₂₅₆ (see above)
84. digital (0, 0, 32640)-net over F₂₅₆ (see above)
85. digital (0, 0, 32640)-net over F₂₅₆ (see above)
86. digital (0, 0, 32640)-net over F₂₅₆ (see above)
87. digital (0, 0, 32640)-net over F₂₅₆ (see above)
88. digital (0, 0, 32640)-net over F₂₅₆ (see above)
89. digital (0, 0, 32640)-net over F₂₅₆ (see above)
90. digital (0, 0, 32640)-net over F₂₅₆ (see above)
91. digital (0, 0, 32640)-net over F₂₅₆ (see above)
92. digital (0, 0, 32640)-net over F₂₅₆ (see above)
93. digital (0, 0, 32640)-net over F₂₅₆ (see above)
94. digital (0, 0, 32640)-net over F₂₅₆ (see above)
95. digital (0, 0, 32640)-net over F₂₅₆ (see above)
96. digital (0, 0, 32640)-net over F₂₅₆ (see above)
97. digital (0, 0, 32640)-net over F₂₅₆ (see above)
98. digital (0, 0, 32640)-net over F₂₅₆ (see above)
99. digital (0, 0, 32640)-net over F₂₅₆ (see above)
100. digital (0, 0, 32640)-net over F₂₅₆ (see above)
101. digital (0, 0, 32640)-net over F₂₅₆ (see above)
102. digital (0, 0, 32640)-net over F₂₅₆ (see above)
103. digital (0, 0, 32640)-net over F₂₅₆ (see above)
104. digital (0, 0, 32640)-net over F₂₅₆ (see above)
105. digital (0, 0, 32640)-net over F₂₅₆ (see above)
106. digital (0, 0, 32640)-net over F₂₅₆ (see above)
107. digital (0, 0, 32640)-net over F₂₅₆ (see above)
108. digital (0, 0, 32640)-net over F₂₅₆ (see above)
109. digital (0, 0, 32640)-net over F₂₅₆ (see above)
110. digital (0, 0, 32640)-net over F₂₅₆ (see above)
111. digital (0, 0, 32640)-net over F₂₅₆ (see above)
112. digital (0, 0, 32640)-net over F₂₅₆ (see above)
113. digital (0, 0, 32640)-net over F₂₅₆ (see above)
114. digital (0, 0, 32640)-net over F₂₅₆ (see above)
115. digital (0, 0, 32640)-net over F₂₅₆ (see above)
116. digital (0, 0, 32640)-net over F₂₅₆ (see above)
117. digital (0, 0, 32640)-net over F₂₅₆ (see above)
118. digital (0, 0, 32640)-net over F₂₅₆ (see above)
119. digital (0, 0, 32640)-net over F₂₅₆ (see above)
120. digital (0, 0, 32640)-net over F₂₅₆ (see above)
121. digital (0, 0, 32640)-net over F₂₅₆ (see above)
122. digital (0, 0, 32640)-net over F₂₅₆ (see above)
123. digital (0, 0, 32640)-net over F₂₅₆ (see above)
124. digital (0, 0, 32640)-net over F₂₅₆ (see above)
125. digital (0, 0, 32640)-net over F₂₅₆ (see above)
126. digital (0, 0, 32640)-net over F₂₅₆ (see above)
127. digital (0, 0, 32640)-net over F₂₅₆ (see above)
128. digital (0, 0, 32640)-net over F₂₅₆ (see above)
129. digital (0, 0, 32640)-net over F₂₅₆ (see above)
130. digital (0, 0, 32640)-net over F₂₅₆ (see above)
131. digital (0, 0, 32640)-net over F₂₅₆ (see above)
132. digital (0, 0, 32640)-net over F₂₅₆ (see above)
133. digital (0, 0, 32640)-net over F₂₅₆ (see above)
134. digital (0, 0, 32640)-net over F₂₅₆ (see above)
135. digital (0, 0, 32640)-net over F₂₅₆ (see above)
136. digital (0, 0, 32640)-net over F₂₅₆ (see above)
137. digital (0, 0, 32640)-net over F₂₅₆ (see above)
138. digital (0, 0, 32640)-net over F₂₅₆ (see above)
139. digital (0, 0, 32640)-net over F₂₅₆ (see above)
140. digital (0, 0, 32640)-net over F₂₅₆ (see above)
141. digital (0, 0, 32640)-net over F₂₅₆ (see above)
142. digital (0, 0, 32640)-net over F₂₅₆ (see above)
143. digital (0, 0, 32640)-net over F₂₅₆ (see above)
144. digital (0, 0, 32640)-net over F₂₅₆ (see above)
145. digital (0, 0, 32640)-net over F₂₅₆ (see above)
146. digital (0, 0, 32640)-net over F₂₅₆ (see above)
147. digital (0, 0, 32640)-net over F₂₅₆ (see above)
148. digital (0, 0, 32640)-net over F₂₅₆ (see above)
149. digital (0, 0, 32640)-net over F₂₅₆ (see above)
150. digital (0, 0, 32640)-net over F₂₅₆ (see above)
151. digital (0, 0, 32640)-net over F₂₅₆ (see above)
152. digital (0, 0, 32640)-net over F₂₅₆ (see above)
153. digital (0, 0, 32640)-net over F₂₅₆ (see above)
154. digital (0, 0, 32640)-net over F₂₅₆ (see above)
155. digital (0, 0, 32640)-net over F₂₅₆ (see above)
156. digital (0, 0, 32640)-net over F₂₅₆ (see above)
157. digital (0, 0, 32640)-net over F₂₅₆ (see above)
158. digital (0, 0, 32640)-net over F₂₅₆ (see above)
159. digital (0, 0, 32640)-net over F₂₅₆ (see above)
160. digital (0, 0, 32640)-net over F₂₅₆ (see above)
161. digital (0, 0, 32640)-net over F₂₅₆ (see above)
162. digital (0, 0, 32640)-net over F₂₅₆ (see above)
163. digital (0, 0, 32640)-net over F₂₅₆ (see above)
164. digital (0, 0, 32640)-net over F₂₅₆ (see above)
165. digital (0, 0, 32640)-net over F₂₅₆ (see above)
166. digital (0, 0, 32640)-net over F₂₅₆ (see above)
167. digital (0, 0, 32640)-net over F₂₅₆ (see above)
168. digital (0, 0, 32640)-net over F₂₅₆ (see above)
169. digital (0, 0, 32640)-net over F₂₅₆ (see above)
170. digital (0, 0, 32640)-net over F₂₅₆ (see above)
171. digital (0, 0, 32640)-net over F₂₅₆ (see above)
172. digital (0, 0, 32640)-net over F₂₅₆ (see above)
173. digital (0, 0, 32640)-net over F₂₅₆ (see above)
174. digital (0, 0, 32640)-net over F₂₅₆ (see above)
175. digital (0, 0, 32640)-net over F₂₅₆ (see above)
176. digital (0, 0, 32640)-net over F₂₅₆ (see above)
177. digital (0, 0, 32640)-net over F₂₅₆ (see above)
178. digital (0, 0, 32640)-net over F₂₅₆ (see above)
179. digital (0, 0, 32640)-net over F₂₅₆ (see above)
180. digital (0, 0, 32640)-net over F₂₅₆ (see above)
181. digital (0, 0, 32640)-net over F₂₅₆ (see above)
182. digital (0, 0, 32640)-net over F₂₅₆ (see above)
183. digital (0, 0, 32640)-net over F₂₅₆ (see above)
184. digital (0, 0, 32640)-net over F₂₅₆ (see above)
185. digital (0, 0, 32640)-net over F₂₅₆ (see above)
186. digital (0, 0, 32640)-net over F₂₅₆ (see above)
187. digital (0, 0, 32640)-net over F₂₅₆ (see above)
188. digital (0, 0, 32640)-net over F₂₅₆ (see above)
189. digital (0, 0, 32640)-net over F₂₅₆ (see above)
190. digital (0, 0, 32640)-net over F₂₅₆ (see above)
191. digital (0, 0, 32640)-net over F₂₅₆ (see above)
192. digital (0, 0, 32640)-net over F₂₅₆ (see above)
193. digital (0, 0, 32640)-net over F₂₅₆ (see above)
194. digital (0, 0, 32640)-net over F₂₅₆ (see above)
195. digital (0, 0, 32640)-net over F₂₅₆ (see above)
196. digital (0, 0, 32640)-net over F₂₅₆ (see above)
197. digital (0, 0, 32640)-net over F₂₅₆ (see above)
198. digital (0, 0, 32640)-net over F₂₅₆ (see above)
199. digital (0, 0, 32640)-net over F₂₅₆ (see above)
200. digital (0, 0, 32640)-net over F₂₅₆ (see above)
201. digital (0, 0, 32640)-net over F₂₅₆ (see above)
202. digital (0, 0, 32640)-net over F₂₅₆ (see above)
203. digital (0, 0, 32640)-net over F₂₅₆ (see above)
204. digital (0, 0, 32640)-net over F₂₅₆ (see above)
205. digital (0, 0, 32640)-net over F₂₅₆ (see above)
206. digital (0, 0, 32640)-net over F₂₅₆ (see above)
207. digital (0, 0, 32640)-net over F₂₅₆ (see above)
208. digital (0, 0, 32640)-net over F₂₅₆ (see above)
209. digital (0, 0, 32640)-net over F₂₅₆ (see above)
210. digital (0, 0, 32640)-net over F₂₅₆ (see above)
211. digital (0, 0, 32640)-net over F₂₅₆ (see above)
212. digital (0, 0, 32640)-net over F₂₅₆ (see above)
213. digital (0, 0, 32640)-net over F₂₅₆ (see above)
214. digital (0, 0, 32640)-net over F₂₅₆ (see above)
215. digital (0, 0, 32640)-net over F₂₅₆ (see above)
216. digital (0, 0, 32640)-net over F₂₅₆ (see above)
217. digital (0, 0, 32640)-net over F₂₅₆ (see above)
218. digital (0, 0, 32640)-net over F₂₅₆ (see above)
219. digital (0, 0, 32640)-net over F₂₅₆ (see above)
220. digital (0, 0, 32640)-net over F₂₅₆ (see above)
221. digital (0, 0, 32640)-net over F₂₅₆ (see above)
222. digital (0, 0, 32640)-net over F₂₅₆ (see above)
223. digital (0, 0, 32640)-net over F₂₅₆ (see above)
224. digital (0, 0, 32640)-net over F₂₅₆ (see above)
225. digital (0, 0, 32640)-net over F₂₅₆ (see above)
226. digital (0, 0, 32640)-net over F₂₅₆ (see above)
227. digital (0, 0, 32640)-net over F₂₅₆ (see above)
228. digital (0, 0, 32640)-net over F₂₅₆ (see above)
229. digital (0, 0, 32640)-net over F₂₅₆ (see above)
230. digital (0, 0, 32640)-net over F₂₅₆ (see above)
231. digital (0, 0, 32640)-net over F₂₅₆ (see above)
232. digital (0, 0, 32640)-net over F₂₅₆ (see above)
233. digital (0, 0, 32640)-net over F₂₅₆ (see above)
234. digital (0, 0, 32640)-net over F₂₅₆ (see above)
235. digital (0, 0, 32640)-net over F₂₅₆ (see above)
236. digital (0, 0, 32640)-net over F₂₅₆ (see above)
237. digital (0, 0, 32640)-net over F₂₅₆ (see above)
238. digital (0, 0, 32640)-net over F₂₅₆ (see above)
239. digital (0, 0, 32640)-net over F₂₅₆ (see above)
240. digital (0, 0, 32640)-net over F₂₅₆ (see above)
241. digital (0, 0, 32640)-net over F₂₅₆ (see above)
242. digital (0, 0, 32640)-net over F₂₅₆ (see above)
243. digital (0, 0, 32640)-net over F₂₅₆ (see above)
244. digital (0, 0, 32640)-net over F₂₅₆ (see above)
245. digital (0, 0, 32640)-net over F₂₅₆ (see above)
246. digital (0, 0, 32640)-net over F₂₅₆ (see above)
247. digital (0, 0, 32640)-net over F₂₅₆ (see above)
248. digital (0, 1, 32640)-net over F₂₅₆, using
  - s-reduction based on digital (0, 1, s)-net over F₂₅₆ with arbitrarily large s, using
    - construction for strength kÂ =Â 1 [i]
249. digital (0, 1, 32640)-net over F₂₅₆ (see above)
250. digital (0, 1, 32640)-net over F₂₅₆ (see above)
251. digital (0, 1, 32640)-net over F₂₅₆ (see above)
252. digital (0, 1, 32640)-net over F₂₅₆ (see above)
253. digital (1, 3, 32640)-net over F₂₅₆, using
  - s-reduction based on digital (1, 3, 65793)-net over F₂₅₆, using
    - kÂ =Â 2 construction [i]
254. digital (1, 4, 32640)-net over F₂₅₆, using
  - s-reduction based on digital (1, 4, 65537)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256⁴, 65537, F₂₅₆, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 256) [i]
255. digital (2, 6, 32640)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256⁶, 32640, F₂₅₆, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(256⁶, 65280, F₂₅₆, 4) (dual of [65280, 65274, 5]-code), using
      - 1 times truncation [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
256. digital (14, 23, 65792)-net over F₂₅₆, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (0, 0, 257)-net over F₂₅₆, using
      - s-reduction based on digital (0, 0, s)-net over F₂₅₆ with arbitrarily large s (see above)
    2. digital (0, 0, 257)-net over F₂₅₆ (see above)
    3. digital (0, 0, 257)-net over F₂₅₆ (see above)
    4. digital (0, 0, 257)-net over F₂₅₆ (see above)
    5. digital (0, 0, 257)-net over F₂₅₆ (see above)
    6. digital (0, 0, 257)-net over F₂₅₆ (see above)
    7. digital (0, 0, 257)-net over F₂₅₆ (see above)
    8. digital (0, 0, 257)-net over F₂₅₆ (see above)
    9. digital (0, 0, 257)-net over F₂₅₆ (see above)
    10. digital (0, 0, 257)-net over F₂₅₆ (see above)
    11. digital (0, 0, 257)-net over F₂₅₆ (see above)
    12. digital (0, 0, 257)-net over F₂₅₆ (see above)
    13. digital (0, 0, 257)-net over F₂₅₆ (see above)
    14. digital (0, 0, 257)-net over F₂₅₆ (see above)
    15. digital (0, 0, 257)-net over F₂₅₆ (see above)
    16. digital (0, 0, 257)-net over F₂₅₆ (see above)
    17. digital (0, 0, 257)-net over F₂₅₆ (see above)
    18. digital (0, 0, 257)-net over F₂₅₆ (see above)
    19. digital (0, 0, 257)-net over F₂₅₆ (see above)
    20. digital (0, 0, 257)-net over F₂₅₆ (see above)
    21. digital (0, 0, 257)-net over F₂₅₆ (see above)
    22. digital (0, 0, 257)-net over F₂₅₆ (see above)
    23. digital (0, 0, 257)-net over F₂₅₆ (see above)
    24. digital (0, 0, 257)-net over F₂₅₆ (see above)
    25. digital (0, 0, 257)-net over F₂₅₆ (see above)
    26. digital (0, 0, 257)-net over F₂₅₆ (see above)
    27. digital (0, 0, 257)-net over F₂₅₆ (see above)
    28. digital (0, 0, 257)-net over F₂₅₆ (see above)
    29. digital (0, 0, 257)-net over F₂₅₆ (see above)
    30. digital (0, 0, 257)-net over F₂₅₆ (see above)
    31. digital (0, 0, 257)-net over F₂₅₆ (see above)
    32. digital (0, 0, 257)-net over F₂₅₆ (see above)
    33. digital (0, 0, 257)-net over F₂₅₆ (see above)
    34. digital (0, 0, 257)-net over F₂₅₆ (see above)
    35. digital (0, 0, 257)-net over F₂₅₆ (see above)
    36. digital (0, 0, 257)-net over F₂₅₆ (see above)
    37. digital (0, 0, 257)-net over F₂₅₆ (see above)
    38. digital (0, 0, 257)-net over F₂₅₆ (see above)
    39. digital (0, 0, 257)-net over F₂₅₆ (see above)
    40. digital (0, 0, 257)-net over F₂₅₆ (see above)
    41. digital (0, 0, 257)-net over F₂₅₆ (see above)
    42. digital (0, 0, 257)-net over F₂₅₆ (see above)
    43. digital (0, 0, 257)-net over F₂₅₆ (see above)
    44. digital (0, 0, 257)-net over F₂₅₆ (see above)
    45. digital (0, 0, 257)-net over F₂₅₆ (see above)
    46. digital (0, 0, 257)-net over F₂₅₆ (see above)
    47. digital (0, 0, 257)-net over F₂₅₆ (see above)
    48. digital (0, 0, 257)-net over F₂₅₆ (see above)
    49. digital (0, 0, 257)-net over F₂₅₆ (see above)
    50. digital (0, 0, 257)-net over F₂₅₆ (see above)
    51. digital (0, 0, 257)-net over F₂₅₆ (see above)
    52. digital (0, 0, 257)-net over F₂₅₆ (see above)
    53. digital (0, 0, 257)-net over F₂₅₆ (see above)
    54. digital (0, 0, 257)-net over F₂₅₆ (see above)
    55. digital (0, 0, 257)-net over F₂₅₆ (see above)
    56. digital (0, 0, 257)-net over F₂₅₆ (see above)
    57. digital (0, 0, 257)-net over F₂₅₆ (see above)
    58. digital (0, 0, 257)-net over F₂₅₆ (see above)
    59. digital (0, 0, 257)-net over F₂₅₆ (see above)
    60. digital (0, 0, 257)-net over F₂₅₆ (see above)
    61. digital (0, 0, 257)-net over F₂₅₆ (see above)
    62. digital (0, 0, 257)-net over F₂₅₆ (see above)
    63. digital (0, 0, 257)-net over F₂₅₆ (see above)
    64. digital (0, 0, 257)-net over F₂₅₆ (see above)
    65. digital (0, 0, 257)-net over F₂₅₆ (see above)
    66. digital (0, 0, 257)-net over F₂₅₆ (see above)
    67. digital (0, 0, 257)-net over F₂₅₆ (see above)
    68. digital (0, 0, 257)-net over F₂₅₆ (see above)
    69. digital (0, 0, 257)-net over F₂₅₆ (see above)
    70. digital (0, 0, 257)-net over F₂₅₆ (see above)
    71. digital (0, 0, 257)-net over F₂₅₆ (see above)
    72. digital (0, 0, 257)-net over F₂₅₆ (see above)
    73. digital (0, 0, 257)-net over F₂₅₆ (see above)
    74. digital (0, 0, 257)-net over F₂₅₆ (see above)
    75. digital (0, 0, 257)-net over F₂₅₆ (see above)
    76. digital (0, 0, 257)-net over F₂₅₆ (see above)
    77. digital (0, 0, 257)-net over F₂₅₆ (see above)
    78. digital (0, 0, 257)-net over F₂₅₆ (see above)
    79. digital (0, 0, 257)-net over F₂₅₆ (see above)
    80. digital (0, 0, 257)-net over F₂₅₆ (see above)
    81. digital (0, 0, 257)-net over F₂₅₆ (see above)
    82. digital (0, 0, 257)-net over F₂₅₆ (see above)
    83. digital (0, 0, 257)-net over F₂₅₆ (see above)
    84. digital (0, 0, 257)-net over F₂₅₆ (see above)
    85. digital (0, 0, 257)-net over F₂₅₆ (see above)
    86. digital (0, 0, 257)-net over F₂₅₆ (see above)
    87. digital (0, 0, 257)-net over F₂₅₆ (see above)
    88. digital (0, 0, 257)-net over F₂₅₆ (see above)
    89. digital (0, 0, 257)-net over F₂₅₆ (see above)
    90. digital (0, 0, 257)-net over F₂₅₆ (see above)
    91. digital (0, 0, 257)-net over F₂₅₆ (see above)
    92. digital (0, 0, 257)-net over F₂₅₆ (see above)
    93. digital (0, 0, 257)-net over F₂₅₆ (see above)
    94. digital (0, 0, 257)-net over F₂₅₆ (see above)
    95. digital (0, 0, 257)-net over F₂₅₆ (see above)
    96. digital (0, 0, 257)-net over F₂₅₆ (see above)
    97. digital (0, 0, 257)-net over F₂₅₆ (see above)
    98. digital (0, 0, 257)-net over F₂₅₆ (see above)
    99. digital (0, 0, 257)-net over F₂₅₆ (see above)
    100. digital (0, 0, 257)-net over F₂₅₆ (see above)
    101. digital (0, 0, 257)-net over F₂₅₆ (see above)
    102. digital (0, 0, 257)-net over F₂₅₆ (see above)
    103. digital (0, 0, 257)-net over F₂₅₆ (see above)
    104. digital (0, 0, 257)-net over F₂₅₆ (see above)
    105. digital (0, 0, 257)-net over F₂₅₆ (see above)
    106. digital (0, 0, 257)-net over F₂₅₆ (see above)
    107. digital (0, 0, 257)-net over F₂₅₆ (see above)
    108. digital (0, 0, 257)-net over F₂₅₆ (see above)
    109. digital (0, 0, 257)-net over F₂₅₆ (see above)
    110. digital (0, 0, 257)-net over F₂₅₆ (see above)
    111. digital (0, 0, 257)-net over F₂₅₆ (see above)
    112. digital (0, 0, 257)-net over F₂₅₆ (see above)
    113. digital (0, 0, 257)-net over F₂₅₆ (see above)
    114. digital (0, 0, 257)-net over F₂₅₆ (see above)
    115. digital (0, 0, 257)-net over F₂₅₆ (see above)
    116. digital (0, 0, 257)-net over F₂₅₆ (see above)
    117. digital (0, 0, 257)-net over F₂₅₆ (see above)
    118. digital (0, 0, 257)-net over F₂₅₆ (see above)
    119. digital (0, 0, 257)-net over F₂₅₆ (see above)
    120. digital (0, 0, 257)-net over F₂₅₆ (see above)
    121. digital (0, 0, 257)-net over F₂₅₆ (see above)
    122. digital (0, 0, 257)-net over F₂₅₆ (see above)
    123. digital (0, 0, 257)-net over F₂₅₆ (see above)
    124. digital (0, 0, 257)-net over F₂₅₆ (see above)
    125. digital (0, 0, 257)-net over F₂₅₆ (see above)
    126. digital (0, 0, 257)-net over F₂₅₆ (see above)
    127. digital (0, 0, 257)-net over F₂₅₆ (see above)
    128. digital (0, 0, 257)-net over F₂₅₆ (see above)
    129. digital (0, 0, 257)-net over F₂₅₆ (see above)
    130. digital (0, 0, 257)-net over F₂₅₆ (see above)
    131. digital (0, 0, 257)-net over F₂₅₆ (see above)
    132. digital (0, 0, 257)-net over F₂₅₆ (see above)
    133. digital (0, 0, 257)-net over F₂₅₆ (see above)
    134. digital (0, 0, 257)-net over F₂₅₆ (see above)
    135. digital (0, 0, 257)-net over F₂₅₆ (see above)
    136. digital (0, 0, 257)-net over F₂₅₆ (see above)
    137. digital (0, 0, 257)-net over F₂₅₆ (see above)
    138. digital (0, 0, 257)-net over F₂₅₆ (see above)
    139. digital (0, 0, 257)-net over F₂₅₆ (see above)
    140. digital (0, 0, 257)-net over F₂₅₆ (see above)
    141. digital (0, 0, 257)-net over F₂₅₆ (see above)
    142. digital (0, 0, 257)-net over F₂₅₆ (see above)
    143. digital (0, 0, 257)-net over F₂₅₆ (see above)
    144. digital (0, 0, 257)-net over F₂₅₆ (see above)
    145. digital (0, 0, 257)-net over F₂₅₆ (see above)
    146. digital (0, 0, 257)-net over F₂₅₆ (see above)
    147. digital (0, 0, 257)-net over F₂₅₆ (see above)
    148. digital (0, 0, 257)-net over F₂₅₆ (see above)
    149. digital (0, 0, 257)-net over F₂₅₆ (see above)
    150. digital (0, 0, 257)-net over F₂₅₆ (see above)
    151. digital (0, 0, 257)-net over F₂₅₆ (see above)
    152. digital (0, 0, 257)-net over F₂₅₆ (see above)
    153. digital (0, 0, 257)-net over F₂₅₆ (see above)
    154. digital (0, 0, 257)-net over F₂₅₆ (see above)
    155. digital (0, 0, 257)-net over F₂₅₆ (see above)
    156. digital (0, 0, 257)-net over F₂₅₆ (see above)
    157. digital (0, 0, 257)-net over F₂₅₆ (see above)
    158. digital (0, 0, 257)-net over F₂₅₆ (see above)
    159. digital (0, 0, 257)-net over F₂₅₆ (see above)
    160. digital (0, 0, 257)-net over F₂₅₆ (see above)
    161. digital (0, 0, 257)-net over F₂₅₆ (see above)
    162. digital (0, 0, 257)-net over F₂₅₆ (see above)
    163. digital (0, 0, 257)-net over F₂₅₆ (see above)
    164. digital (0, 0, 257)-net over F₂₅₆ (see above)
    165. digital (0, 0, 257)-net over F₂₅₆ (see above)
    166. digital (0, 0, 257)-net over F₂₅₆ (see above)
    167. digital (0, 0, 257)-net over F₂₅₆ (see above)
    168. digital (0, 0, 257)-net over F₂₅₆ (see above)
    169. digital (0, 0, 257)-net over F₂₅₆ (see above)
    170. digital (0, 0, 257)-net over F₂₅₆ (see above)
    171. digital (0, 0, 257)-net over F₂₅₆ (see above)
    172. digital (0, 0, 257)-net over F₂₅₆ (see above)
    173. digital (0, 0, 257)-net over F₂₅₆ (see above)
    174. digital (0, 0, 257)-net over F₂₅₆ (see above)
    175. digital (0, 0, 257)-net over F₂₅₆ (see above)
    176. digital (0, 0, 257)-net over F₂₅₆ (see above)
    177. digital (0, 0, 257)-net over F₂₅₆ (see above)
    178. digital (0, 0, 257)-net over F₂₅₆ (see above)
    179. digital (0, 0, 257)-net over F₂₅₆ (see above)
    180. digital (0, 0, 257)-net over F₂₅₆ (see above)
    181. digital (0, 0, 257)-net over F₂₅₆ (see above)
    182. digital (0, 0, 257)-net over F₂₅₆ (see above)
    183. digital (0, 0, 257)-net over F₂₅₆ (see above)
    184. digital (0, 0, 257)-net over F₂₅₆ (see above)
    185. digital (0, 0, 257)-net over F₂₅₆ (see above)
    186. digital (0, 0, 257)-net over F₂₅₆ (see above)
    187. digital (0, 0, 257)-net over F₂₅₆ (see above)
    188. digital (0, 0, 257)-net over F₂₅₆ (see above)
    189. digital (0, 0, 257)-net over F₂₅₆ (see above)
    190. digital (0, 0, 257)-net over F₂₅₆ (see above)
    191. digital (0, 0, 257)-net over F₂₅₆ (see above)
    192. digital (0, 0, 257)-net over F₂₅₆ (see above)
    193. digital (0, 0, 257)-net over F₂₅₆ (see above)
    194. digital (0, 0, 257)-net over F₂₅₆ (see above)
    195. digital (0, 0, 257)-net over F₂₅₆ (see above)
    196. digital (0, 0, 257)-net over F₂₅₆ (see above)
    197. digital (0, 0, 257)-net over F₂₅₆ (see above)
    198. digital (0, 0, 257)-net over F₂₅₆ (see above)
    199. digital (0, 0, 257)-net over F₂₅₆ (see above)
    200. digital (0, 0, 257)-net over F₂₅₆ (see above)
    201. digital (0, 0, 257)-net over F₂₅₆ (see above)
    202. digital (0, 0, 257)-net over F₂₅₆ (see above)
    203. digital (0, 0, 257)-net over F₂₅₆ (see above)
    204. digital (0, 0, 257)-net over F₂₅₆ (see above)
    205. digital (0, 0, 257)-net over F₂₅₆ (see above)
    206. digital (0, 0, 257)-net over F₂₅₆ (see above)
    207. digital (0, 0, 257)-net over F₂₅₆ (see above)
    208. digital (0, 0, 257)-net over F₂₅₆ (see above)
    209. digital (0, 0, 257)-net over F₂₅₆ (see above)
    210. digital (0, 0, 257)-net over F₂₅₆ (see above)
    211. digital (0, 0, 257)-net over F₂₅₆ (see above)
    212. digital (0, 0, 257)-net over F₂₅₆ (see above)
    213. digital (0, 0, 257)-net over F₂₅₆ (see above)
    214. digital (0, 0, 257)-net over F₂₅₆ (see above)
    215. digital (0, 0, 257)-net over F₂₅₆ (see above)
    216. digital (0, 0, 257)-net over F₂₅₆ (see above)
    217. digital (0, 0, 257)-net over F₂₅₆ (see above)
    218. digital (0, 0, 257)-net over F₂₅₆ (see above)
    219. digital (0, 0, 257)-net over F₂₅₆ (see above)
    220. digital (0, 0, 257)-net over F₂₅₆ (see above)
    221. digital (0, 0, 257)-net over F₂₅₆ (see above)
    222. digital (0, 0, 257)-net over F₂₅₆ (see above)
    223. digital (0, 0, 257)-net over F₂₅₆ (see above)
    224. digital (0, 0, 257)-net over F₂₅₆ (see above)
    225. digital (0, 0, 257)-net over F₂₅₆ (see above)
    226. digital (0, 0, 257)-net over F₂₅₆ (see above)
    227. digital (0, 0, 257)-net over F₂₅₆ (see above)
    228. digital (0, 0, 257)-net over F₂₅₆ (see above)
    229. digital (0, 0, 257)-net over F₂₅₆ (see above)
    230. digital (0, 0, 257)-net over F₂₅₆ (see above)
    231. digital (0, 0, 257)-net over F₂₅₆ (see above)
    232. digital (0, 0, 257)-net over F₂₅₆ (see above)
    233. digital (0, 0, 257)-net over F₂₅₆ (see above)
    234. digital (0, 0, 257)-net over F₂₅₆ (see above)
    235. digital (0, 0, 257)-net over F₂₅₆ (see above)
    236. digital (0, 0, 257)-net over F₂₅₆ (see above)
    237. digital (0, 0, 257)-net over F₂₅₆ (see above)
    238. digital (0, 0, 257)-net over F₂₅₆ (see above)
    239. digital (0, 0, 257)-net over F₂₅₆ (see above)
    240. digital (0, 0, 257)-net over F₂₅₆ (see above)
    241. digital (0, 0, 257)-net over F₂₅₆ (see above)
    242. digital (0, 0, 257)-net over F₂₅₆ (see above)
    243. digital (0, 0, 257)-net over F₂₅₆ (see above)
    244. digital (0, 0, 257)-net over F₂₅₆ (see above)
    245. digital (0, 0, 257)-net over F₂₅₆ (see above)
    246. digital (0, 0, 257)-net over F₂₅₆ (see above)
    247. digital (0, 0, 257)-net over F₂₅₆ (see above)
    248. digital (0, 1, 257)-net over F₂₅₆, using
      - s-reduction based on digital (0, 1, s)-net over F₂₅₆ with arbitrarily large s (see above)
    249. digital (0, 1, 257)-net over F₂₅₆ (see above)
    250. digital (0, 1, 257)-net over F₂₅₆ (see above)
    251. digital (0, 1, 257)-net over F₂₅₆ (see above)
    252. digital (0, 1, 257)-net over F₂₅₆ (see above)
    253. digital (0, 2, 257)-net over F₂₅₆, using
      - kÂ =Â 2 construction [i]
    254. digital (0, 3, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
    255. digital (0, 4, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
    256. digital (0, 9, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(32, 41, large)-Net in Base 256 — Upper bound on s

There is no (32, 41, large)-net in base 256, because

7 times m-reduction [i] would yield (32, 34, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]

Best Known (32, 41, s)-Nets in Base 256

(32, 41, large)-Net over F256 — Constructive and digital

(32, 41, large)-Net in Base 256 — Upper bound on s

(32, 41, large)-Net over F₂₅₆ — Constructive and digital