MinT - Information on Result #1192516

Information on Result #1192516

Digital (71, 94, 746)-net over F₈, using net defined by OOA based on linear OOA(8⁹⁴, 746, F₈, 23, 23) (dual of [(746, 23), 17064, 24]-NRT-code), using

OOA 11-folding and stacking with additional row [i] based on linear OA(8⁹⁴, 8207, F₈, 23) (dual of [8207, 8113, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁹⁴, 8208, F₈, 23) (dual of [8208, 8114, 24]-code), using
  - trace code [i] based on linear OA(64⁴⁷, 4104, F₆₄, 23) (dual of [4104, 4057, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(19) [i] based on
      1. linear OA(64⁴⁵, 4096, F₆₄, 23) (dual of [4096, 4051, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(64³⁹, 4096, F₆₄, 20) (dual of [4096, 4057, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(64², 8, F₆₄, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
        discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [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 (72, 95, 746)-net over F₈	[i]	Net Duplication
2	Digital (73, 96, 746)-net over F₈	[i]
3	Digital (74, 97, 746)-net over F₈	[i]
4	Digital (71, 93, 746)-net over F₈	[i]	m-Reduction