MinT - Information on Result #1195498

Information on Result #1195498

Digital (67, 88, 13109)-net over F₁₆, using net defined by OOA based on linear OOA(16⁸⁸, 13109, F₁₆, 21, 21) (dual of [(13109, 21), 275201, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(16⁸⁸, 131091, F₁₆, 21) (dual of [131091, 131003, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁸⁸, 131096, F₁₆, 21) (dual of [131096, 131008, 22]-code), using
  - trace code [i] based on linear OA(256⁴⁴, 65548, F₂₅₆, 21) (dual of [65548, 65504, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(256³³, 65537, F₂₅₆, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
        discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
        Reedâ€“Solomon code RS(253,256) [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		This result only	Method
1	Digital (68, 89, 13109)-net over F₁₆	[i]		Net Duplication
2	Digital (69, 90, 13109)-net over F₁₆	[i]		Net Duplication