MinT - Information on Result #1192602

Information on Result #1192602

Digital (116, 140, 43691)-net over F₈, using net defined by OOA based on linear OOA(8¹⁴⁰, 43691, F₈, 24, 24) (dual of [(43691, 24), 1048444, 25]-NRT-code), using

OA 12-folding and stacking [i] based on linear OA(8¹⁴⁰, 524292, F₈, 24) (dual of [524292, 524152, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹⁴⁰, 524294, F₈, 24) (dual of [524294, 524154, 25]-code), using
  - trace code [i] based on linear OA(64⁷⁰, 262147, F₆₄, 24) (dual of [262147, 262077, 25]-code), using
    - constructionÂ X applied to C_e(23) âŠ‚ C_e(22) [i] based on
      1. linear OA(64⁷⁰, 262144, F₆₄, 24) (dual of [262144, 262074, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
      2. linear OA(64⁶⁷, 262144, F₆₄, 23) (dual of [262144, 262077, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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 (117, 141, 43691)-net over F₈	[i]	Net Duplication
2	Digital (118, 142, 43691)-net over F₈	[i]
3	Digital (119, 143, 43691)-net over F₈	[i]