MinT - Information on Result #1198826

Information on Result #1198826

Digital (18, 25, 349526)-net over F₃₂, using net defined by OOA based on linear OOA(32²⁵, 349526, F₃₂, 7, 7) (dual of [(349526, 7), 2446657, 8]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OA(32²⁵, 1048579, F₃₂, 7) (dual of [1048579, 1048554, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(32²⁵, 1048580, F₃₂, 7) (dual of [1048580, 1048555, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(32²⁵, 1048576, F₃₂, 7) (dual of [1048576, 1048551, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(32²¹, 1048576, F₃₂, 6) (dual of [1048576, 1048555, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    3. linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 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]

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 (21, 28, 349559)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
2	Digital (22, 29, 350551)-net over F₃₂	[i]
3	Digital (23, 30, 352662)-net over F₃₂	[i]
4	Digital (77, 91, 1547897)-net over F₃₂	[i]
5	Digital (81, 96, 1547897)-net over F₃₂	[i]
6	(75, 89, 1547897)-net in base 32	[i]
7	(79, 94, 1547897)-net in base 32	[i]
8	Digital (34, 41, large)-net over F₃₂	[i]	Generalized (u,Â u+v)-Construction for Nets