MinT - Information on Result #1199192

Information on Result #1199192

Digital (12, 25, 171)-net over F₃₂, using net defined by OOA based on linear OOA(32²⁵, 171, F₃₂, 13, 13) (dual of [(171, 13), 2198, 14]-NRT-code), using

OOA 6-folding and stacking with additional row [i] based on linear OA(32²⁵, 1027, F₃₂, 13) (dual of [1027, 1002, 14]-code), using
- constructionÂ XX applied to C₁Â =Â C([1022,10]), C₂Â =Â C([0,11]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,10]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([1022,11]) [i] based on
  1. linear OA(32²³, 1023, F₃₂, 12) (dual of [1023, 1000, 13]-code), using the primitive BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â {−1,0,…,10}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  2. linear OA(32²³, 1023, F₃₂, 12) (dual of [1023, 1000, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(32²⁵, 1023, F₃₂, 13) (dual of [1023, 998, 14]-code), using the primitive BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â {−1,0,…,11}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  4. linear OA(32²¹, 1023, F₃₂, 11) (dual of [1023, 1002, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  5. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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(32⁰, 2, F₃₂, 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 (13, 26, 171)-net over F₃₂	[i]	Net Duplication
2	Digital (12, 24, 171)-net over F₃₂	[i]	m-Reduction
3	Digital (18, 31, 204)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
4	Digital (19, 32, 215)-net over F₃₂	[i]
5	Digital (21, 34, 237)-net over F₃₂	[i]
6	Digital (22, 35, 248)-net over F₃₂	[i]
7	Digital (44, 70, 256)-net over F₃₂	[i]
8	Digital (45, 71, 262)-net over F₃₂	[i]
9	Digital (46, 72, 284)-net over F₃₂	[i]
10	Digital (48, 74, 324)-net over F₃₂	[i]
11	Digital (44, 71, 256)-net over F₃₂	[i]
12	Digital (45, 72, 262)-net over F₃₂	[i]
13	Digital (46, 73, 284)-net over F₃₂	[i]
14	Digital (48, 75, 324)-net over F₃₂	[i]
15	Digital (50, 77, 345)-net over F₃₂	[i]
16	Digital (77, 104, 2691)-net over F₃₂	[i]