MinT - Information on Result #1204800

Information on Result #1204800

Digital (21, 40, 7283)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁴⁰, 7283, F₂₅₆, 19, 19) (dual of [(7283, 19), 138337, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(256⁴⁰, 65548, F₂₅₆, 19) (dual of [65548, 65508, 20]-code), using
- constructionÂ X applied to C([0,9]) âŠ‚ C([0,7]) [i] based on
  1. linear OA(256³⁷, 65537, F₂₅₆, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
  2. linear OA(256²⁹, 65537, F₂₅₆, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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		Method
1	Digital (22, 40, 7283)-net over F₂₅₆	[i]	t-Expansion
2	Digital (22, 41, 7283)-net over F₂₅₆	[i]	Net Duplication
3	Digital (23, 42, 7283)-net over F₂₅₆	[i]
4	Digital (24, 43, 7283)-net over F₂₅₆	[i]
5	Digital (21, 39, 7283)-net over F₂₅₆	[i]	m-Reduction
6	(45, 64, 7283)-net in base 32	[i]	Base Change