MinT - Information on Result #1195764

Information on Result #1195764

Digital (95, 126, 8739)-net over F₁₆, using net defined by OOA based on linear OOA(16¹²⁶, 8739, F₁₆, 31, 31) (dual of [(8739, 31), 270783, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(16¹²⁶, 131086, F₁₆, 31) (dual of [131086, 130960, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹²⁶, 131088, F₁₆, 31) (dual of [131088, 130962, 32]-code), using
  - trace code [i] based on linear OA(256⁶³, 65544, F₂₅₆, 31) (dual of [65544, 65481, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(27) [i] based on
      1. linear OA(256⁶¹, 65536, F₂₅₆, 31) (dual of [65536, 65475, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
        discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
        Reedâ€“Solomon code RS(254,256) [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 (96, 127, 8739)-net over F₁₆	[i]	Net Duplication
2	Digital (97, 128, 8739)-net over F₁₆	[i]
3	Digital (98, 129, 8739)-net over F₁₆	[i]
4	Digital (99, 130, 8739)-net over F₁₆	[i]
5	Digital (95, 125, 8739)-net over F₁₆	[i]	m-Reduction