MinT - Information on Result #1192518

Information on Result #1192518

Digital (75, 98, 747)-net over F₈, using net defined by OOA based on linear OOA(8⁹⁸, 747, F₈, 23, 23) (dual of [(747, 23), 17083, 24]-NRT-code), using

OOA 11-folding and stacking with additional row [i] based on linear OA(8⁹⁸, 8218, F₈, 23) (dual of [8218, 8120, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁹⁸, 8220, F₈, 23) (dual of [8220, 8122, 24]-code), using
  - trace code [i] based on linear OA(64⁴⁹, 4110, F₆₄, 23) (dual of [4110, 4061, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(17) [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(64³⁵, 4096, F₆₄, 18) (dual of [4096, 4061, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. linear OA(64⁴, 14, F₆₄, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
        discarding factors / shortening the dual code based on linear OA(64⁴, 64, F₆₄, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
        Reedâ€“Solomon code RS(60,64) [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 (76, 99, 747)-net over F₈	[i]		Net Duplication
2	Digital (77, 100, 747)-net over F₈	[i]		Net Duplication