MinT - Information on Result #1195610

Information on Result #1195610

Digital (70, 94, 10923)-net over F₁₆, using net defined by OOA based on linear OOA(16⁹⁴, 10923, F₁₆, 24, 24) (dual of [(10923, 24), 262058, 25]-NRT-code), using

OA 12-folding and stacking [i] based on linear OA(16⁹⁴, 131076, F₁₆, 24) (dual of [131076, 130982, 25]-code), using
- trace code [i] based on linear OA(256⁴⁷, 65538, F₂₅₆, 24) (dual of [65538, 65491, 25]-code), using
  - constructionÂ X applied to C_e(23) âŠ‚ C_e(22) [i] based on
    1. linear OA(256⁴⁷, 65536, F₂₅₆, 24) (dual of [65536, 65489, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    2. linear OA(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (71, 95, 10923)-net over F₁₆	[i]	Net Duplication
2	Digital (72, 96, 10923)-net over F₁₆	[i]
3	Digital (73, 97, 10923)-net over F₁₆	[i]
4	Digital (82, 106, 10940)-net over F₁₆	[i]	(u,Â u+v)-Construction for Nets
5	Digital (83, 107, 10947)-net over F₁₆	[i]
6	Digital (84, 108, 10956)-net over F₁₆	[i]
7	Digital (85, 109, 10961)-net over F₁₆	[i]
8	Digital (86, 110, 10968)-net over F₁₆	[i]