MinT - Information on Result #1197482

Information on Result #1197482

Digital (9, 19, 146)-net over F₂₇, using net defined by OOA based on linear OOA(27¹⁹, 146, F₂₇, 10, 10) (dual of [(146, 10), 1441, 11]-NRT-code), using

OA 5-folding and stacking [i] based on linear OA(27¹⁹, 730, F₂₇, 10) (dual of [730, 711, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(27¹⁹, 731, F₂₇, 10) (dual of [731, 712, 11]-code), using
  - constructionÂ X applied to C_e(9) âŠ‚ C_e(8) [i] based on
    1. linear OA(27¹⁹, 729, F₂₇, 10) (dual of [729, 710, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    2. linear OA(27¹⁷, 729, F₂₇, 9) (dual of [729, 712, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    3. linear OA(27⁰, 2, F₂₇, 0) (dual of [2, 2, 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 (14, 24, 174)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
2	Digital (15, 25, 184)-net over F₂₇	[i]
3	Digital (16, 26, 292)-net over F₂₇	[i]
4	Digital (28, 48, 176)-net over F₂₇	[i]
5	Digital (29, 49, 188)-net over F₂₇	[i]
6	Digital (30, 50, 192)-net over F₂₇	[i]
7	Digital (34, 54, 204)-net over F₂₇	[i]
8	Digital (35, 55, 224)-net over F₂₇	[i]
9	Digital (36, 56, 232)-net over F₂₇	[i]
10	Digital (28, 49, 176)-net over F₂₇	[i]
11	Digital (29, 50, 188)-net over F₂₇	[i]
12	Digital (30, 51, 192)-net over F₂₇	[i]
13	Digital (34, 55, 204)-net over F₂₇	[i]
14	Digital (35, 56, 224)-net over F₂₇	[i]
15	Digital (36, 57, 232)-net over F₂₇	[i]
16	Digital (37, 58, 256)-net over F₂₇	[i]
17	Digital (38, 59, 264)-net over F₂₇	[i]
18	Digital (59, 80, 2114)-net over F₂₇	[i]
19	Digital (79, 100, 53290)-net over F₂₇	[i]