MinT - Information on Result #3278211

Information on Result #3278211

(36, 56, 6554)-net in base 64, using t-expansion based on (35, 56, 6554)-net in base 64, using

base change [i] based on digital (21, 42, 6554)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁴², 6554, F₂₅₆, 21, 21) (dual of [(6554, 21), 137592, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(256⁴², 65541, F₂₅₆, 21) (dual of [65541, 65499, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(256⁴², 65542, F₂₅₆, 21) (dual of [65542, 65500, 22]-code), using
      - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
        linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        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]
        linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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	(37, 57, 6554)-net in base 64	[i]		Net Duplication