MinT - Information on Result #1201926

Information on Result #1201926

Digital (55, 82, 20166)-net over F₆₄, using net defined by OOA based on linear OOA(64⁸², 20166, F₆₄, 27, 27) (dual of [(20166, 27), 544400, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(64⁸², 262159, F₆₄, 27) (dual of [262159, 262077, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁸², 262160, F₆₄, 27) (dual of [262160, 262078, 28]-code), using
  - constructionÂ X applied to C([0,13]) âŠ‚ C([0,11]) [i] based on
    1. 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]
    2. linear OA(64⁶⁷, 262145, F₆₄, 23) (dual of [262145, 262078, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
    3. linear OA(64³, 15, F₆₄, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-cap in PG(2,64)), using
      - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [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 (56, 83, 20166)-net over F₆₄	[i]	Net Duplication
2	Digital (57, 84, 20166)-net over F₆₄	[i]
3	Digital (58, 85, 20166)-net over F₆₄	[i]
4	Digital (55, 81, 20166)-net over F₆₄	[i]	m-Reduction
5	(96, 123, 20166)-net in base 16	[i]	Base Change