MinT - Information on Result #1190868

Information on Result #1190868

Digital (70, 91, 1681)-net over F₇, using net defined by OOA based on linear OOA(7⁹¹, 1681, F₇, 21, 21) (dual of [(1681, 21), 35210, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(7⁹¹, 16811, F₇, 21) (dual of [16811, 16720, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁹¹, 16812, F₇, 21) (dual of [16812, 16721, 22]-code), using
  - 1 times truncation [i] based on linear OA(7⁹², 16813, F₇, 22) (dual of [16813, 16721, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(19) [i] based on
      1. linear OA(7⁹¹, 16807, F₇, 22) (dual of [16807, 16716, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. 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]
      3. linear OA(7¹, 6, F₇, 1) (dual of [6, 5, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (71, 92, 1681)-net over F₇	[i]	Net Duplication
2	Digital (72, 93, 1681)-net over F₇	[i]	Net Duplication
3	Digital (81, 102, 1694)-net over F₇	[i]	(u,Â u+v)-Construction for Nets