MinT - Information on Result #1192708

Information on Result #1192708

Digital (107, 133, 20165)-net over F₈, using net defined by OOA based on linear OOA(8¹³³, 20165, F₈, 26, 26) (dual of [(20165, 26), 524157, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(8¹³³, 262145, F₈, 26) (dual of [262145, 262012, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹³³, 262150, F₈, 26) (dual of [262150, 262017, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
    1. linear OA(8¹³³, 262144, F₈, 26) (dual of [262144, 262011, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(8¹²⁷, 262144, F₈, 25) (dual of [262144, 262017, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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 (108, 134, 20165)-net over F₈	[i]	Net Duplication
2	Digital (109, 135, 20165)-net over F₈	[i]	Net Duplication
3	Digital (120, 146, 20174)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
4	Digital (121, 147, 20179)-net over F₈	[i]
5	Digital (122, 148, 20182)-net over F₈	[i]
6	Digital (123, 149, 20189)-net over F₈	[i]
7	Digital (124, 150, 20190)-net over F₈	[i]
8	Digital (125, 151, 20193)-net over F₈	[i]