MinT - Information on Result #1192092

Information on Result #1192092

Digital (88, 106, 233017)-net over F₈, using net defined by OOA based on linear OOA(8¹⁰⁶, 233017, F₈, 18, 18) (dual of [(233017, 18), 4194200, 19]-NRT-code), using

OA 9-folding and stacking [i] based on linear OA(8¹⁰⁶, 2097153, F₈, 18) (dual of [2097153, 2097047, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹⁰⁶, 2097159, F₈, 18) (dual of [2097159, 2097053, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(8¹⁰⁶, 2097152, F₈, 18) (dual of [2097152, 2097046, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(8⁹⁹, 2097152, F₈, 17) (dual of [2097152, 2097053, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 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 (89, 107, 233017)-net over F₈	[i]	Net Duplication
2	Digital (97, 115, 233026)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
3	Digital (98, 116, 233031)-net over F₈	[i]
4	Digital (99, 117, 233034)-net over F₈	[i]
5	Digital (100, 118, 233041)-net over F₈	[i]
6	Digital (101, 119, 233042)-net over F₈	[i]
7	Digital (102, 120, 233045)-net over F₈	[i]