MinT - Information on Result #1198802

Information on Result #1198802

Digital (6, 13, 342)-net over F₃₂, using net defined by OOA based on linear OOA(32¹³, 342, F₃₂, 7, 7) (dual of [(342, 7), 2381, 8]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OA(32¹³, 1027, F₃₂, 7) (dual of [1027, 1014, 8]-code), using
- constructionÂ XX applied to C₁Â =Â C([1022,4]), C₂Â =Â C([0,5]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,4]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([1022,5]) [i] based on
  1. linear OA(32¹¹, 1023, F₃₂, 6) (dual of [1023, 1012, 7]-code), using the primitive BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â {−1,0,…,4}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  2. linear OA(32¹¹, 1023, F₃₂, 6) (dual of [1023, 1012, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  3. linear OA(32¹³, 1023, F₃₂, 7) (dual of [1023, 1010, 8]-code), using the primitive BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â {−1,0,…,5}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  4. linear OA(32⁹, 1023, F₃₂, 5) (dual of [1023, 1014, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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 (10, 17, 684)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
2	Digital (20, 34, 196)-net over F₃₂	[i]
3	Digital (22, 36, 208)-net over F₃₂	[i]
4	Digital (24, 38, 240)-net over F₃₂	[i]
5	Digital (65, 79, 1198713)-net over F₃₂	[i]
6	Digital (20, 35, 196)-net over F₃₂	[i]
7	Digital (22, 37, 208)-net over F₃₂	[i]
8	Digital (24, 39, 240)-net over F₃₂	[i]
9	Digital (26, 41, 256)-net over F₃₂	[i]
10	Digital (41, 56, 5023)-net over F₃₂	[i]
11	Digital (55, 70, 150139)-net over F₃₂	[i]
12	Digital (69, 84, 1198713)-net over F₃₂	[i]
13	(63, 77, 1198713)-net in base 32	[i]
14	(67, 82, 1198713)-net in base 32	[i]
15	Digital (59, 90, 392)-net over F₃₂	[i]	Generalized (u,Â u+v)-Construction for Nets