MinT - Information on Result #1201948

Information on Result #1201948

Digital (57, 86, 18725)-net over F₆₄, using net defined by OOA based on linear OOA(64⁸⁶, 18725, F₆₄, 29, 29) (dual of [(18725, 29), 542939, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(64⁸⁶, 262151, F₆₄, 29) (dual of [262151, 262065, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁸⁶, 262152, F₆₄, 29) (dual of [262152, 262066, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,13]) [i] based on
    1. linear OA(64⁸⁵, 262145, F₆₄, 29) (dual of [262145, 262060, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(64⁷⁹, 262145, F₆₄, 27) (dual of [262145, 262066, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    3. linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (58, 86, 18725)-net over F₆₄	[i]	t-Expansion
2	Digital (58, 87, 18725)-net over F₆₄	[i]	Net Duplication
3	Digital (59, 88, 18725)-net over F₆₄	[i]
4	Digital (60, 89, 18725)-net over F₆₄	[i]
5	Digital (57, 85, 18725)-net over F₆₄	[i]	m-Reduction
6	(100, 129, 18725)-net in base 16	[i]	Base Change