MinT - Information on Result #1197334

Information on Result #1197334

Digital (7, 15, 183)-net over F₂₇, using net defined by OOA based on linear OOA(27¹⁵, 183, F₂₇, 8, 8) (dual of [(183, 8), 1449, 9]-NRT-code), using

OA 4-folding and stacking [i] based on linear OA(27¹⁵, 732, F₂₇, 8) (dual of [732, 717, 9]-code), using
- constructionÂ XX applied to C₁Â =Â C([727,5]), C₂Â =Â C([0,6]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,5]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([727,6]) [i] based on
  1. linear OA(27¹³, 728, F₂₇, 7) (dual of [728, 715, 8]-code), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,…,5}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  2. linear OA(27¹³, 728, F₂₇, 7) (dual of [728, 715, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  3. linear OA(27¹⁵, 728, F₂₇, 8) (dual of [728, 713, 9]-code), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,…,6}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  4. linear OA(27¹¹, 728, F₂₇, 6) (dual of [728, 717, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  5. 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]
  6. linear OA(27⁰, 2, F₂₇, 0) (dual of [2, 2, 1]-code) (see above)

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 (8, 16, 183)-net over F₂₇	[i]	Net Duplication
2	Digital (11, 19, 211)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (22, 38, 164)-net over F₂₇	[i]
4	Digital (23, 39, 168)-net over F₂₇	[i]
5	Digital (24, 40, 176)-net over F₂₇	[i]
6	Digital (25, 41, 188)-net over F₂₇	[i]
7	Digital (26, 42, 192)-net over F₂₇	[i]
8	Digital (28, 44, 204)-net over F₂₇	[i]
9	Digital (75, 91, 1048758)-net over F₂₇	[i]
10	Digital (22, 39, 164)-net over F₂₇	[i]
11	Digital (23, 40, 168)-net over F₂₇	[i]
12	Digital (24, 41, 176)-net over F₂₇	[i]
13	Digital (25, 42, 188)-net over F₂₇	[i]
14	Digital (26, 43, 192)-net over F₂₇	[i]
15	Digital (28, 45, 204)-net over F₂₇	[i]
16	Digital (29, 46, 224)-net over F₂₇	[i]
17	Digital (30, 47, 232)-net over F₂₇	[i]
18	Digital (47, 64, 2643)-net over F₂₇	[i]
19	Digital (63, 80, 66613)-net over F₂₇	[i]
20	Digital (79, 96, 1048758)-net over F₂₇	[i]
21	(26, 43, 300)-net in base 27	[i]