MinT - Information on Result #1824583

Information on Result #1824583

(49, 84, 964)-net in base 64, using base change based on digital (37, 72, 964)-net over F₁₂₈, using

128² times duplication [i] based on digital (35, 70, 964)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁷⁰, 964, F₁₂₈, 35, 35) (dual of [(964, 35), 33670, 36]-NRT-code), using
  - OOA 17-folding and stacking with additional row [i] based on linear OA(128⁷⁰, 16389, F₁₂₈, 35) (dual of [16389, 16319, 36]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁷⁰, 16390, F₁₂₈, 35) (dual of [16390, 16320, 36]-code), using
      - constructionÂ X applied to C([0,17]) âŠ‚ C([0,16]) [i] based on
        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]
        linear OA(128⁶⁵, 16385, F₁₂₈, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
        linear OA(128¹, 5, F₁₂₈, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 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	(50, 84, 964)-net in base 64	[i]		t-Expansion
2	(50, 85, 964)-net in base 64	[i]		Net Duplication
3	(51, 86, 964)-net in base 64	[i]
4	(52, 87, 964)-net in base 64	[i]
5	(53, 88, 964)-net in base 64	[i]
6	(49, 83, 964)-net in base 64	[i]		m-Reduction