MinT - Information on Result #1200044

Information on Result #1200044

Digital (53, 80, 2521)-net over F₃₂, using net defined by OOA based on linear OOA(32⁸⁰, 2521, F₃₂, 27, 27) (dual of [(2521, 27), 67987, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(32⁸⁰, 32774, F₃₂, 27) (dual of [32774, 32694, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁸⁰, 32776, F₃₂, 27) (dual of [32776, 32696, 28]-code), using
  - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(32⁷⁹, 32769, F₃₂, 27) (dual of [32769, 32690, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    2. linear OA(32⁷³, 32769, F₃₂, 25) (dual of [32769, 32696, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. linear OA(32¹, 7, F₃₂, 1) (dual of [7, 6, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 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 (54, 81, 2521)-net over F₃₂	[i]	Net Duplication
2	Digital (55, 82, 2521)-net over F₃₂	[i]	Net Duplication
3	Digital (53, 79, 2521)-net over F₃₂	[i]	m-Reduction
4	Digital (67, 94, 2565)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
5	Digital (69, 96, 2585)-net over F₃₂	[i]
6	Digital (71, 98, 2597)-net over F₃₂	[i]
7	Digital (73, 100, 2619)-net over F₃₂	[i]
8	(73, 100, 2521)-net in base 16	[i]	Base Change