MinT - Information on Result #1197846

Information on Result #1197846

Digital (28, 43, 2812)-net over F₂₇, using net defined by OOA based on linear OOA(27⁴³, 2812, F₂₇, 15, 15) (dual of [(2812, 15), 42137, 16]-NRT-code), using

OOA 7-folding and stacking with additional row [i] based on linear OA(27⁴³, 19685, F₂₇, 15) (dual of [19685, 19642, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁴³, 19686, F₂₇, 15) (dual of [19686, 19643, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
    1. linear OA(27⁴³, 19683, F₂₇, 15) (dual of [19683, 19640, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(27⁴⁰, 19683, F₂₇, 14) (dual of [19683, 19643, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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 (29, 44, 2812)-net over F₂₇	[i]	Net Duplication
2	Digital (35, 50, 2840)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (36, 51, 2850)-net over F₂₇	[i]
4	Digital (37, 52, 2860)-net over F₂₇	[i]
5	Digital (38, 53, 2868)-net over F₂₇	[i]
6	Digital (39, 54, 2878)-net over F₂₇	[i]
7	Digital (40, 55, 2888)-net over F₂₇	[i]
8	Digital (41, 56, 3055)-net over F₂₇	[i]
9	Digital (40, 55, 2896)-net over F₂₇	[i]
10	(38, 53, 2894)-net in base 27	[i]
11	(39, 54, 2912)-net in base 27	[i]
12	(40, 55, 2928)-net in base 27	[i]