MinT - Information on Result #1204970

Information on Result #1204970

Digital (31, 56, 5463)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁵⁶, 5463, F₂₅₆, 25, 25) (dual of [(5463, 25), 136519, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(256⁵⁶, 65557, F₂₅₆, 25) (dual of [65557, 65501, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(256⁵⁶, 65560, F₂₅₆, 25) (dual of [65560, 65504, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(256⁴⁹, 65537, F₂₅₆, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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(256⁷, 23, F₂₅₆, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁷, 256, F₂₅₆, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
        Reedâ€“Solomon code RS(249,256) [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 (32, 56, 5463)-net over F₂₅₆	[i]	t-Expansion
2	Digital (32, 57, 5463)-net over F₂₅₆	[i]	Net Duplication
3	Digital (33, 58, 5463)-net over F₂₅₆	[i]
4	Digital (34, 59, 5463)-net over F₂₅₆	[i]
5	Digital (31, 55, 5463)-net over F₂₅₆	[i]	m-Reduction
6	(39, 64, 5463)-net in base 128	[i]	Base Change