MinT - Information on Result #1200196

Information on Result #1200196

Digital (72, 107, 1929)-net over F₃₂, using net defined by OOA based on linear OOA(32¹⁰⁷, 1929, F₃₂, 35, 35) (dual of [(1929, 35), 67408, 36]-NRT-code), using

OOA 17-folding and stacking with additional row [i] based on linear OA(32¹⁰⁷, 32794, F₃₂, 35) (dual of [32794, 32687, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32¹⁰⁷, 32796, F₃₂, 35) (dual of [32796, 32689, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(26) [i] based on
    1. linear OA(32¹⁰⁰, 32768, F₃₂, 35) (dual of [32768, 32668, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(32⁷⁹, 32768, F₃₂, 27) (dual of [32768, 32689, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    3. linear OA(32⁷, 28, F₃₂, 7) (dual of [28, 21, 8]-code or 28-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 (73, 107, 1929)-net over F₃₂	[i]	t-Expansion
2	Digital (73, 108, 1929)-net over F₃₂	[i]	Net Duplication
3	Digital (74, 109, 1929)-net over F₃₂	[i]
4	Digital (75, 110, 1929)-net over F₃₂	[i]
5	Digital (72, 106, 1929)-net over F₃₂	[i]	m-Reduction