MinT - Information on Result #1192222

Information on Result #1192222

Digital (94, 113, 233017)-net over F₈, using net defined by OOA based on linear OOA(8¹¹³, 233017, F₈, 19, 19) (dual of [(233017, 19), 4427210, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(8¹¹³, 2097154, F₈, 19) (dual of [2097154, 2097041, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹¹³, 2097159, F₈, 19) (dual of [2097159, 2097046, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
    1. linear OA(8¹¹³, 2097152, F₈, 19) (dual of [2097152, 2097039, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. 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]
    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 (103, 122, 233026)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
2	Digital (104, 123, 233031)-net over F₈	[i]
3	Digital (105, 124, 233034)-net over F₈	[i]
4	Digital (106, 125, 233041)-net over F₈	[i]
5	Digital (107, 126, 233042)-net over F₈	[i]
6	Digital (108, 127, 233045)-net over F₈	[i]
7	(109, 128, 233050)-net in base 8	[i]