MinT - Information on Result #1197588

Information on Result #1197588

Digital (11, 23, 122)-net over F₂₇, using net defined by OOA based on linear OOA(27²³, 122, F₂₇, 12, 12) (dual of [(122, 12), 1441, 13]-NRT-code), using

OA 6-folding and stacking [i] based on linear OA(27²³, 732, F₂₇, 12) (dual of [732, 709, 13]-code), using
- constructionÂ XX applied to C₁Â =Â C([727,9]), C₂Â =Â C([0,10]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,9]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([727,10]) [i] based on
  1. linear OA(27²¹, 728, F₂₇, 11) (dual of [728, 707, 12]-code), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  2. linear OA(27²¹, 728, F₂₇, 11) (dual of [728, 707, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  3. linear OA(27²³, 728, F₂₇, 12) (dual of [728, 705, 13]-code), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,…,10}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  4. linear OA(27¹⁹, 728, F₂₇, 10) (dual of [728, 709, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (12, 24, 122)-net over F₂₇	[i]	Net Duplication
2	Digital (19, 31, 170)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (20, 32, 178)-net over F₂₇	[i]
4	Digital (40, 64, 204)-net over F₂₇	[i]
5	Digital (41, 65, 224)-net over F₂₇	[i]
6	Digital (42, 66, 232)-net over F₂₇	[i]
7	Digital (43, 67, 250)-net over F₂₇	[i]
8	Digital (44, 68, 254)-net over F₂₇	[i]
9	Digital (40, 65, 204)-net over F₂₇	[i]
10	Digital (41, 66, 224)-net over F₂₇	[i]
11	Digital (42, 67, 232)-net over F₂₇	[i]
12	Digital (43, 68, 250)-net over F₂₇	[i]
13	Digital (44, 69, 254)-net over F₂₇	[i]
14	Digital (45, 70, 262)-net over F₂₇	[i]
15	Digital (46, 71, 268)-net over F₂₇	[i]
16	Digital (71, 96, 1762)-net over F₂₇	[i]