MinT - Information on Result #1824767

Information on Result #1824767

(19, 32, 10924)-net in base 128, using base change based on digital (15, 28, 10924)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256²⁸, 10924, F₂₅₆, 13, 13) (dual of [(10924, 13), 141984, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(256²⁸, 65545, F₂₅₆, 13) (dual of [65545, 65517, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(256²⁸, 65548, F₂₅₆, 13) (dual of [65548, 65520, 14]-code), using
    - constructionÂ X applied to C([0,6]) âŠ‚ C([0,4]) [i] based on
      1. linear OA(256²⁵, 65537, F₂₅₆, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      2. linear OA(256¹⁷, 65537, F₂₅₆, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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.

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	(20, 33, 10924)-net in base 128	[i]		Net Duplication
2	(21, 34, 10924)-net in base 128	[i]		Net Duplication