MinT - Information on Result #1179532

Information on Result #1179532

Digital (15, 19, 131075)-net over F₈, using net defined by OOA based on linear OOA(8¹⁹, 131075, F₈, 4, 4) (dual of [(131075, 4), 524281, 5]-NRT-code), using

appending kth column [i] based on linear OOA(8¹⁹, 131075, F₈, 3, 4) (dual of [(131075, 3), 393206, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8¹⁹, 262150, F₈, 4) (dual of [262150, 262131, 5]-code), using
  - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
    1. linear OA(8¹⁹, 262144, F₈, 4) (dual of [262144, 262125, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    2. linear OA(8¹³, 262144, F₈, 3) (dual of [262144, 262131, 4]-code or 262144-cap in PG(12,8)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
    3. linear OA(8⁰, 6, F₈, 0) (dual of [6, 6, 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 (69, 77, 4325375)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
2	Digital (76, 85, 4325375)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
3	Digital (150, 163, 5723493)-net over F₈	[i]	Generalized (u,Â u+v)-Construction for Nets
4	Digital (151, 164, 5723549)-net over F₈	[i]
5	Digital (152, 165, 5723605)-net over F₈	[i]
6	Digital (152, 165, 5723692)-net over F₈	[i]
7	Digital (143, 155, 5723493)-net over F₈	[i]
8	Digital (144, 156, 5723549)-net over F₈	[i]
9	Digital (145, 157, 5723605)-net over F₈	[i]
10	Digital (145, 157, 5723692)-net over F₈	[i]
11	Digital (148, 161, 5723484)-net over F₈	[i]
12	Digital (149, 162, 5723540)-net over F₈	[i]
13	Digital (150, 163, 5723683)-net over F₈	[i]
14	Digital (141, 153, 5723484)-net over F₈	[i]
15	Digital (142, 154, 5723540)-net over F₈	[i]
16	Digital (143, 155, 5723683)-net over F₈	[i]
17	Digital (145, 158, 5723475)-net over F₈	[i]
18	Digital (138, 150, 5723475)-net over F₈	[i]