MinT - Information on Result #3178645

Information on Result #3178645

Digital (19, 35, 8193)-net over F₂₅₆, using 1 times m-reduction based on digital (19, 36, 8193)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256³⁶, 8193, F₂₅₆, 17, 17) (dual of [(8193, 17), 139245, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(256³⁶, 65545, F₂₅₆, 17) (dual of [65545, 65509, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(256³⁶, 65548, F₂₅₆, 17) (dual of [65548, 65512, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
      1. 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]
      2. 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]
      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	(40, 56, 8193)-net in base 32	[i]		Base Change
2	(24, 40, 8193)-net in base 128	[i]		Base Change