MinT - Information on Result #3248797

Information on Result #3248797

Digital (38, 66, 4683)-net over F₂₅₆, using t-expansion based on digital (37, 66, 4683)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256⁶⁶, 4683, F₂₅₆, 29, 29) (dual of [(4683, 29), 135741, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(256⁶⁶, 65563, F₂₅₆, 29) (dual of [65563, 65497, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁶⁶, 65566, F₂₅₆, 29) (dual of [65566, 65500, 30]-code), using
    - constructionÂ X applied to C([0,14]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
      2. 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]
      3. linear OA(256⁹, 29, F₂₅₆, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁹, 256, F₂₅₆, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
        Reedâ€“Solomon code RS(247,256) [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 (39, 67, 4683)-net over F₂₅₆	[i]		Net Duplication