MinT - Information on Result #1195378

Information on Result #1195378

Digital (81, 98, 2097150)-net over F₁₆, using net defined by OOA based on linear OOA(16⁹⁸, 2097150, F₁₆, 18, 17) (dual of [(2097150, 18), 37748602, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(16⁹⁸, 8388601, F₁₆, 2, 17) (dual of [(8388601, 2), 16777104, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16⁹⁸, 8388602, F₁₆, 2, 17) (dual of [(8388602, 2), 16777106, 18]-NRT-code), using
  - trace code [i] based on linear OOA(256⁴⁹, 4194301, F₂₅₆, 2, 17) (dual of [(4194301, 2), 8388553, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(256⁴⁹, 8388602, F₂₅₆, 17) (dual of [8388602, 8388553, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(256⁴⁹, large, F₂₅₆, 17) (dual of [large, large−49, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (82, 98, 2097150)-net over F₁₆	[i]	t-Expansion
2	Digital (82, 99, 2097150)-net over F₁₆	[i]	Net Duplication
3	Digital (83, 100, 2097150)-net over F₁₆	[i]
4	Digital (84, 101, 2097150)-net over F₁₆	[i]
5	Digital (85, 102, 2097150)-net over F₁₆	[i]
6	Digital (86, 103, 2097150)-net over F₁₆	[i]
7	Digital (87, 104, 2097150)-net over F₁₆	[i]
8	Digital (88, 105, 2097150)-net over F₁₆	[i]
9	Digital (81, 97, 2097150)-net over F₁₆	[i]	m-Reduction
10	Digital (179, 196, 4194300)-net over F₄	[i]	Trace Code for Nets
11	Digital (89, 106, 2097167)-net over F₁₆	[i]	(u,Â u+v)-Construction for Nets
12	Digital (90, 107, 2097174)-net over F₁₆	[i]
13	Digital (91, 108, 2097183)-net over F₁₆	[i]
14	Digital (92, 109, 2097188)-net over F₁₆	[i]
15	Digital (93, 110, 2097195)-net over F₁₆	[i]
16	Digital (94, 111, 2097199)-net over F₁₆	[i]
17	Digital (95, 112, 2097215)-net over F₁₆	[i]
18	Digital (96, 113, 2097407)-net over F₁₆	[i]
19	Digital (97, 114, 2097664)-net over F₁₆	[i]
20	Digital (99, 116, 2097666)-net over F₁₆	[i]
21	Digital (101, 118, 2097681)-net over F₁₆	[i]
22	Digital (102, 119, 2097688)-net over F₁₆	[i]
23	Digital (103, 120, 2098174)-net over F₁₆	[i]
24	Digital (104, 121, 2098175)-net over F₁₆	[i]
25	Digital (105, 122, 2098178)-net over F₁₆	[i]
26	Digital (107, 124, 2098191)-net over F₁₆	[i]
27	Digital (108, 125, 2098198)-net over F₁₆	[i]
28	Digital (109, 126, 2098690)-net over F₁₆	[i]
29	Digital (110, 127, 2113535)-net over F₁₆	[i]
30	Digital (111, 128, 2129919)-net over F₁₆	[i]
31	Digital (113, 130, 2129920)-net over F₁₆	[i]
32	Digital (107, 124, 2098195)-net over F₁₆	[i]
33	Digital (108, 125, 2098451)-net over F₁₆	[i]
34	Digital (109, 126, 2098692)-net over F₁₆	[i]
35	(93, 110, 2097215)-net in base 16	[i]
36	(95, 112, 2097279)-net in base 16	[i]
37	(102, 119, 2097697)-net in base 16	[i]
38	(106, 123, 2098206)-net in base 16	[i]
39	(108, 125, 2101246)-net in base 16	[i]
40	(109, 126, 2105342)-net in base 16	[i]