MinT - Best Known (70−10, 70, s)-Nets in Base 32

Best Known (70−10, 70, s)-Nets in Base 32

(70−10, 70, 3355473)-Net over F₃₂ — Constructive and digital

Digital (60, 70, 3355473)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 3, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
      - the rational function field F₃₂(x) [i]
    - Niederreiter sequence [i]
2. digital (16, 21, 1677720)-net over F₃₂, using
  - s-reduction based on digital (16, 21, 4194301)-net over F₃₂, using
    - net defined by OOA [i] based on linear OOA(32²¹, 4194301, F₃₂, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(32²¹, large, F₃₂, 5) (dual of [large, large−21, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
3. digital (36, 46, 1677720)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32⁴⁶, 1677720, F₃₂, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
    - OA 5-folding and stacking [i] based on linear OA(32⁴⁶, 8388600, F₃₂, 10) (dual of [8388600, 8388554, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁴⁶, large, F₃₂, 10) (dual of [large, large−46, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

(70−10, 70, 3355648)-Net in Base 32 — Constructive

(60, 70, 3355648)-net in base 32, using

base change [i] based on (40, 50, 3355648)-net in base 128, using
- 128² times duplication [i] based on (38, 48, 3355648)-net in base 128, using
  - base change [i] based on digital (32, 42, 3355648)-net over F₂₅₆, using
    - generalized (u,Â u+v)-construction [i] based on
      1. digital (0, 0, 13108)-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, 13108)-net over F₂₅₆ (see above)
      3. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      4. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      5. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      6. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      7. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      8. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      9. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      10. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      11. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      12. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      13. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      14. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      15. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      16. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      17. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      18. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      19. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      20. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      21. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      22. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      23. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      24. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      25. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      26. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      27. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      28. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      29. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      30. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      31. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      32. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      33. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      34. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      35. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      36. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      37. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      38. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      39. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      40. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      41. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      42. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      43. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      44. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      45. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      46. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      47. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      48. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      49. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      50. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      51. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      52. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      53. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      54. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      55. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      56. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      57. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      58. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      59. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      60. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      61. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      62. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      63. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      64. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      65. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      66. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      67. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      68. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      69. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      70. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      71. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      72. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      73. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      74. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      75. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      76. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      77. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      78. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      79. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      80. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      81. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      82. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      83. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      84. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      85. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      86. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      87. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      88. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      89. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      90. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      91. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      92. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      93. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      94. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      95. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      96. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      97. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      98. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      99. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      100. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      101. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      102. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      103. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      104. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      105. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      106. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      107. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      108. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      109. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      110. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      111. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      112. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      113. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      114. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      115. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      116. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      117. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      118. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      119. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      120. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      121. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      122. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      123. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      124. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      125. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      126. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      127. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      128. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      129. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      130. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      131. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      132. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      133. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      134. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      135. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      136. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      137. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      138. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      139. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      140. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      141. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      142. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      143. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      144. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      145. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      146. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      147. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      148. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      149. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      150. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      151. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      152. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      153. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      154. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      155. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      156. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      157. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      158. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      159. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      160. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      161. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      162. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      163. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      164. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      165. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      166. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      167. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      168. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      169. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      170. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      171. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      172. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      173. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      174. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      175. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      176. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      177. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      178. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      179. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      180. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      181. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      182. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      183. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      184. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      185. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      186. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      187. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      188. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      189. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      190. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      191. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      192. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      193. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      194. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      195. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      196. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      197. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      198. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      199. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      200. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      201. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      202. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      203. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      204. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      205. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      206. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      207. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      208. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      209. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      210. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      211. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      212. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      213. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      214. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      215. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      216. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      217. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      218. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      219. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      220. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      221. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      222. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      223. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      224. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      225. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      226. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      227. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      228. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      229. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      230. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      231. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      232. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      233. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      234. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      235. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      236. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      237. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      238. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      239. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      240. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      241. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      242. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      243. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      244. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      245. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      246. digital (0, 0, 13108)-net over F₂₅₆ (see above)
      247. digital (0, 1, 13108)-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]
      248. digital (0, 1, 13108)-net over F₂₅₆ (see above)
      249. digital (0, 1, 13108)-net over F₂₅₆ (see above)
      250. digital (0, 1, 13108)-net over F₂₅₆ (see above)
      251. digital (0, 1, 13108)-net over F₂₅₆ (see above)
      252. digital (1, 3, 13108)-net over F₂₅₆, using
        s-reduction based on digital (1, 3, 65793)-net over F₂₅₆, using
        kÂ =Â 2 construction [i]
      253. digital (1, 3, 13108)-net over F₂₅₆ (see above)
      254. digital (1, 4, 13108)-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, 7, 13108)-net over F₂₅₆, using
        s-reduction based on digital (2, 7, 32640)-net over F₂₅₆, using
        net defined by OOA [i] based on linear OOA(256⁷, 32640, F₂₅₆, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [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 (10, 20, 13108)-net over F₂₅₆, using
        net defined by OOA [i] based on linear OOA(256²⁰, 13108, F₂₅₆, 10, 10) (dual of [(13108, 10), 131060, 11]-NRT-code), using
        OA 5-folding and stacking [i] based on linear OA(256²⁰, 65540, F₂₅₆, 10) (dual of [65540, 65520, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(256²⁰, 65541, F₂₅₆, 10) (dual of [65541, 65521, 11]-code), using
        constructionÂ X applied to C_e(9) âŠ‚ C_e(7) [i] based on
        linear OA(256¹⁹, 65536, F₂₅₆, 10) (dual of [65536, 65517, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
        parity-check code [i]

(70−10, 70, large)-Net over F₃₂ — Digital

Digital (60, 70, large)-net over F₃₂, using

6 times m-reduction [i] based on digital (60, 76, large)-net over F₃₂, using
- Gilbertâ€“VarÅ¡amov bound [i]

(70−10, 70, large)-Net in Base 32 — Upper bound on s

There is no (60, 70, large)-net in base 32, because

8 times m-reduction [i] would yield (60, 62, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]

Best Known (70−10, 70, s)-Nets in Base 32

(70−10, 70, 3355473)-Net over F32 — Constructive and digital

(70−10, 70, 3355648)-Net in Base 32 — Constructive

(70−10, 70, large)-Net over F32 — Digital

(70−10, 70, large)-Net in Base 32 — Upper bound on s

(70−10, 70, 3355473)-Net over F₃₂ — Constructive and digital

(70−10, 70, large)-Net over F₃₂ — Digital