MinT - Information on Result #1200108

Information on Result #1200108

Digital (61, 90, 2342)-net over F₃₂, using net defined by OOA based on linear OOA(32⁹⁰, 2342, F₃₂, 29, 29) (dual of [(2342, 29), 67828, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(32⁹⁰, 32789, F₃₂, 29) (dual of [32789, 32699, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁹⁰, 32792, F₃₂, 29) (dual of [32792, 32702, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,11]) [i] based on
    1. linear OA(32⁸⁵, 32769, F₃₂, 29) (dual of [32769, 32684, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(32⁶⁷, 32769, F₃₂, 23) (dual of [32769, 32702, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
    3. linear OA(32⁵, 23, F₃₂, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,32)), using
      - discarding factors / shortening the dual code based on linear OA(32⁵, 32, F₃₂, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
        Reedâ€“Solomon code RS(27,32) [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 (62, 90, 2342)-net over F₃₂	[i]	t-Expansion
2	Digital (62, 91, 2342)-net over F₃₂	[i]	Net Duplication
3	Digital (63, 92, 2342)-net over F₃₂	[i]
4	Digital (64, 93, 2342)-net over F₃₂	[i]
5	Digital (61, 89, 2342)-net over F₃₂	[i]	m-Reduction