MinT - Information on Result #1192376

Information on Result #1192376

Digital (67, 88, 821)-net over F₈, using net defined by OOA based on linear OOA(8⁸⁸, 821, F₈, 21, 21) (dual of [(821, 21), 17153, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(8⁸⁸, 8211, F₈, 21) (dual of [8211, 8123, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁸⁸, 8216, F₈, 21) (dual of [8216, 8128, 22]-code), using
  - trace code [i] based on linear OA(64⁴⁴, 4108, F₆₄, 21) (dual of [4108, 4064, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(64⁴¹, 4097, F₆₄, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(64³³, 4097, F₆₄, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(64³, 11, F₆₄, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
        discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [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 (68, 89, 821)-net over F₈	[i]		Net Duplication
2	Digital (69, 90, 821)-net over F₈	[i]		Net Duplication