MinT - Information on Result #1841683

Information on Result #1841683

(54, 89, 965)-net in base 64, using net defined by OOA based on OOA(64⁸⁹, 965, S₆₄, 35, 35), using

OOA 17-folding and stacking with additional row [i] based on OA(64⁸⁹, 16406, S₆₄, 35), using
- discarding factors based on OA(64⁸⁹, 16408, S₆₄, 35), using
  - discarding parts of the base [i] based on linear OA(128⁷⁶, 16408, F₁₂₈, 35) (dual of [16408, 16332, 36]-code), using
    - constructionÂ X applied to C([0,17]) âŠ‚ C([0,13]) [i] based on
      1. linear OA(128⁶⁹, 16385, F₁₂₈, 35) (dual of [16385, 16316, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]
      2. linear OA(128⁵³, 16385, F₁₂₈, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      3. linear OA(128⁷, 23, F₁₂₈, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
        discarding factors / shortening the dual code based on linear OA(128⁷, 128, F₁₂₈, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
        Reedâ€“Solomon code RS(121,128) [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	(55, 89, 965)-net in base 64	[i]		t-Expansion
2	(55, 90, 965)-net in base 64	[i]		Net Duplication
3	(54, 88, 965)-net in base 64	[i]		m-Reduction