MinT - Information on Result #1199976

Information on Result #1199976

Digital (55, 80, 2733)-net over F₃₂, using net defined by OOA based on linear OOA(32⁸⁰, 2733, F₃₂, 25, 25) (dual of [(2733, 25), 68245, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(32⁸⁰, 32797, F₃₂, 25) (dual of [32797, 32717, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁸⁰, 32800, F₃₂, 25) (dual of [32800, 32720, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,8]) [i] based on
    1. 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]
    2. linear OA(32⁴⁹, 32769, F₃₂, 17) (dual of [32769, 32720, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    3. linear OA(32⁷, 31, F₃₂, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,32)), using
      - discarding factors / shortening the dual code based on linear OA(32⁷, 32, F₃₂, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
        Reedâ€“Solomon code RS(25,32) [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 (56, 81, 2733)-net over F₃₂	[i]	Net Duplication
2	Digital (57, 82, 2733)-net over F₃₂	[i]	Net Duplication
3	Digital (55, 79, 2733)-net over F₃₂	[i]	m-Reduction