MinT - Information on Result #1192056

Information on Result #1192056

Digital (58, 76, 3641)-net over F₈, using net defined by OOA based on linear OOA(8⁷⁶, 3641, F₈, 18, 18) (dual of [(3641, 18), 65462, 19]-NRT-code), using

OA 9-folding and stacking [i] based on linear OA(8⁷⁶, 32769, F₈, 18) (dual of [32769, 32693, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁷⁶, 32773, F₈, 18) (dual of [32773, 32697, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(8⁷⁶, 32768, F₈, 18) (dual of [32768, 32692, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(8⁷¹, 32768, F₈, 17) (dual of [32768, 32697, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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 (59, 77, 3641)-net over F₈	[i]	Net Duplication
2	Digital (60, 78, 3641)-net over F₈	[i]	Net Duplication
3	Digital (67, 85, 3650)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
4	Digital (68, 86, 3655)-net over F₈	[i]
5	Digital (69, 87, 3658)-net over F₈	[i]
6	Digital (70, 88, 3665)-net over F₈	[i]
7	Digital (71, 89, 3666)-net over F₈	[i]
8	Digital (72, 90, 3669)-net over F₈	[i]