MinT - Information on Result #1192520

Information on Result #1192520

Digital (78, 101, 2979)-net over F₈, using net defined by OOA based on linear OOA(8¹⁰¹, 2979, F₈, 23, 23) (dual of [(2979, 23), 68416, 24]-NRT-code), using

OOA 11-folding and stacking with additional row [i] based on linear OA(8¹⁰¹, 32770, F₈, 23) (dual of [32770, 32669, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹⁰¹, 32773, F₈, 23) (dual of [32773, 32672, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
    1. linear OA(8¹⁰¹, 32768, F₈, 23) (dual of [32768, 32667, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(8⁹⁶, 32768, F₈, 22) (dual of [32768, 32672, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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 (79, 102, 2979)-net over F₈	[i]	Net Duplication
2	Digital (89, 112, 2988)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
3	Digital (90, 113, 2993)-net over F₈	[i]
4	Digital (91, 114, 2996)-net over F₈	[i]
5	Digital (92, 115, 3003)-net over F₈	[i]
6	Digital (93, 116, 3004)-net over F₈	[i]
7	Digital (94, 117, 3007)-net over F₈	[i]
8	Digital (96, 119, 3013)-net over F₈	[i]
9	Digital (97, 120, 3014)-net over F₈	[i]