MinT - Information on Result #1197534

Information on Result #1197534

Digital (10, 21, 146)-net over F₂₇, using net defined by OOA based on linear OOA(27²¹, 146, F₂₇, 11, 11) (dual of [(146, 11), 1585, 12]-NRT-code), using

OOA 5-folding and stacking with additional row [i] based on linear OA(27²¹, 731, F₂₇, 11) (dual of [731, 710, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
  1. linear OA(27²¹, 729, F₂₇, 11) (dual of [729, 708, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. 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]
  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 (11, 22, 146)-net over F₂₇	[i]	Net Duplication
2	Digital (15, 26, 174)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (17, 28, 292)-net over F₂₇	[i]
4	Digital (37, 59, 204)-net over F₂₇	[i]
5	Digital (38, 60, 224)-net over F₂₇	[i]
6	Digital (39, 61, 232)-net over F₂₇	[i]
7	Digital (40, 62, 256)-net over F₂₇	[i]
8	Digital (37, 60, 204)-net over F₂₇	[i]
9	Digital (38, 61, 224)-net over F₂₇	[i]
10	Digital (39, 62, 232)-net over F₂₇	[i]
11	Digital (40, 63, 256)-net over F₂₇	[i]
12	Digital (41, 64, 264)-net over F₂₇	[i]
13	Digital (42, 65, 280)-net over F₂₇	[i]
14	Digital (65, 88, 1935)-net over F₂₇	[i]
15	Digital (87, 110, 48459)-net over F₂₇	[i]