MinT - Information on Result #1201928

Information on Result #1201928

Digital (59, 86, 20167)-net over F₆₄, using net defined by OOA based on linear OOA(64⁸⁶, 20167, F₆₄, 27, 27) (dual of [(20167, 27), 544423, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(64⁸⁶, 262172, F₆₄, 27) (dual of [262172, 262086, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁸⁶, 262176, F₆₄, 27) (dual of [262176, 262090, 28]-code), using
  - constructionÂ X applied to C([0,13]) âŠ‚ C([0,9]) [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(64⁵⁵, 262145, F₆₄, 19) (dual of [262145, 262090, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(64⁷, 31, F₆₄, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,64)), using
      - discarding factors / shortening the dual code based on linear OA(64⁷, 64, F₆₄, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
        Reedâ€“Solomon code RS(57,64) [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 (60, 87, 20167)-net over F₆₄	[i]	Net Duplication
2	Digital (61, 88, 20167)-net over F₆₄	[i]	Net Duplication
3	Digital (59, 85, 20167)-net over F₆₄	[i]	m-Reduction