MinT - Information on Result #1190832

Information on Result #1190832

Digital (66, 86, 1681)-net over F₇, using net defined by OOA based on linear OOA(7⁸⁶, 1681, F₇, 20, 20) (dual of [(1681, 20), 33534, 21]-NRT-code), using

OA 10-folding and stacking [i] based on linear OA(7⁸⁶, 16810, F₇, 20) (dual of [16810, 16724, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁸⁶, 16812, F₇, 20) (dual of [16812, 16726, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
    1. linear OA(7⁸⁶, 16807, F₇, 20) (dual of [16807, 16721, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(7⁸¹, 16807, F₇, 19) (dual of [16807, 16726, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(7⁰, 5, F₇, 0) (dual of [5, 5, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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 (67, 87, 1681)-net over F₇	[i]	Net Duplication
2	Digital (76, 96, 1689)-net over F₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (77, 97, 1694)-net over F₇	[i]
4	Digital (79, 99, 1695)-net over F₇	[i]
5	Digital (80, 100, 1697)-net over F₇	[i]
6	Digital (81, 101, 1699)-net over F₇	[i]
7	Digital (82, 102, 1702)-net over F₇	[i]