MinT - Information on Result #1197256

Information on Result #1197256

Digital (5, 11, 244)-net over F₂₇, using net defined by OOA based on linear OOA(27¹¹, 244, F₂₇, 6, 6) (dual of [(244, 6), 1453, 7]-NRT-code), using

OA 3-folding and stacking [i] based on linear OA(27¹¹, 732, F₂₇, 6) (dual of [732, 721, 7]-code), using
- constructionÂ XX applied to C₁Â =Â C([727,3]), C₂Â =Â C([0,4]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,3]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([727,4]) [i] based on
  1. linear OA(27⁹, 728, F₂₇, 5) (dual of [728, 719, 6]-code), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,1,2,3}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
  2. linear OA(27⁹, 728, F₂₇, 5) (dual of [728, 719, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
  3. linear OA(27¹¹, 728, F₂₇, 6) (dual of [728, 717, 7]-code), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,…,4}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  4. linear OA(27⁷, 728, F₂₇, 4) (dual of [728, 721, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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 (16, 28, 136)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
2	Digital (17, 29, 152)-net over F₂₇	[i]
3	Digital (18, 30, 164)-net over F₂₇	[i]
4	Digital (19, 31, 168)-net over F₂₇	[i]
5	Digital (20, 32, 176)-net over F₂₇	[i]
6	Digital (55, 67, 1398344)-net over F₂₇	[i]
7	Digital (16, 29, 136)-net over F₂₇	[i]
8	Digital (17, 30, 152)-net over F₂₇	[i]
9	Digital (18, 31, 164)-net over F₂₇	[i]
10	Digital (19, 32, 168)-net over F₂₇	[i]
11	Digital (20, 33, 176)-net over F₂₇	[i]
12	Digital (21, 34, 192)-net over F₂₇	[i]
13	Digital (22, 35, 204)-net over F₂₇	[i]
14	Digital (35, 48, 3524)-net over F₂₇	[i]
15	Digital (47, 60, 88818)-net over F₂₇	[i]
16	Digital (59, 72, 1398344)-net over F₂₇	[i]
17	(18, 30, 232)-net in base 27	[i]
18	(18, 31, 232)-net in base 27	[i]