MinT - Information on Result #1191112

Information on Result #1191112

Digital (31, 38, 174764)-net over F₈, using net defined by OOA based on linear OOA(8³⁸, 174764, F₈, 7, 7) (dual of [(174764, 7), 1223310, 8]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OA(8³⁸, 524293, F₈, 7) (dual of [524293, 524255, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8³⁸, 524294, F₈, 7) (dual of [524294, 524256, 8]-code), using
  - trace code [i] based on linear OA(64¹⁹, 262147, F₆₄, 7) (dual of [262147, 262128, 8]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
      1. linear OA(64¹⁹, 262144, F₆₄, 7) (dual of [262144, 262125, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(64¹⁶, 262144, F₆₄, 6) (dual of [262144, 262128, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (32, 39, 174764)-net over F₈	[i]	Net Duplication
2	Digital (34, 41, 174773)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
3	Digital (35, 42, 174829)-net over F₈	[i]
4	Digital (130, 144, 2571506)-net over F₈	[i]
5	Digital (137, 152, 2571506)-net over F₈	[i]