MinT - Information on Result #1192454

Information on Result #1192454

Digital (68, 90, 746)-net over F₈, using net defined by OOA based on linear OOA(8⁹⁰, 746, F₈, 22, 22) (dual of [(746, 22), 16322, 23]-NRT-code), using

OA 11-folding and stacking [i] based on linear OA(8⁹⁰, 8206, F₈, 22) (dual of [8206, 8116, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁹⁰, 8208, F₈, 22) (dual of [8208, 8118, 23]-code), using
  - trace code [i] based on linear OA(64⁴⁵, 4104, F₆₄, 22) (dual of [4104, 4059, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
      1. linear OA(64⁴³, 4096, F₆₄, 22) (dual of [4096, 4053, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(64³⁷, 4096, F₆₄, 19) (dual of [4096, 4059, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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		This result only	Method
1	Digital (69, 91, 746)-net over F₈	[i]		Net Duplication
2	Digital (70, 92, 746)-net over F₈	[i]		Net Duplication