MinT - Information on Result #1195756

Information on Result #1195756

Digital (96, 126, 8740)-net over F₁₆, using net defined by OOA based on linear OOA(16¹²⁶, 8740, F₁₆, 30, 30) (dual of [(8740, 30), 262074, 31]-NRT-code), using

OA 15-folding and stacking [i] based on linear OA(16¹²⁶, 131100, F₁₆, 30) (dual of [131100, 130974, 31]-code), using
- trace code [i] based on linear OA(256⁶³, 65550, F₂₅₆, 30) (dual of [65550, 65487, 31]-code), using
  - constructionÂ X applied to C_e(29) âŠ‚ C_e(24) [i] based on
    1. linear OA(256⁵⁹, 65536, F₂₅₆, 30) (dual of [65536, 65477, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
    2. linear OA(256⁴⁹, 65536, F₂₅₆, 25) (dual of [65536, 65487, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(256⁴, 14, F₂₅₆, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
        Reedâ€“Solomon code RS(252,256) [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 (97, 127, 8740)-net over F₁₆	[i]	Net Duplication
2	Digital (98, 128, 8740)-net over F₁₆	[i]
3	Digital (99, 129, 8740)-net over F₁₆	[i]
4	Digital (100, 130, 8740)-net over F₁₆	[i]