MinT - Information on Result #1198784

Information on Result #1198784

Digital (15, 21, 349526)-net over F₃₂, using net defined by OOA based on linear OOA(32²¹, 349526, F₃₂, 6, 6) (dual of [(349526, 6), 2097135, 7]-NRT-code), using

OA 3-folding and stacking [i] based on linear OA(32²¹, 1048578, F₃₂, 6) (dual of [1048578, 1048557, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(32²¹, 1048580, F₃₂, 6) (dual of [1048580, 1048559, 7]-code), using
  - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
    1. 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]
    2. linear OA(32¹⁷, 1048576, F₃₂, 5) (dual of [1048576, 1048559, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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 (18, 24, 349559)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
2	Digital (19, 25, 350551)-net over F₃₂	[i]
3	Digital (65, 77, 1747626)-net over F₃₂	[i]
4	Digital (69, 82, 1747626)-net over F₃₂	[i]
5	(63, 75, 1747626)-net in base 32	[i]
6	(67, 80, 1747626)-net in base 32	[i]
7	Digital (94, 107, 5592416)-net over F₃₂	[i]	Generalized (u,Â u+v)-Construction for Nets
8	Digital (95, 108, 5592448)-net over F₃₂	[i]
9	Digital (97, 110, 5592480)-net over F₃₂	[i]
10	Digital (90, 102, 5592416)-net over F₃₂	[i]
11	Digital (91, 103, 5592448)-net over F₃₂	[i]
12	Digital (92, 104, 5592480)-net over F₃₂	[i]
13	Digital (94, 106, 5592512)-net over F₃₂	[i]
14	Digital (95, 107, 5592544)-net over F₃₂	[i]
15	Digital (96, 108, 5593472)-net over F₃₂	[i]
16	Digital (97, 109, 5593824)-net over F₃₂	[i]
17	Digital (98, 110, 5593856)-net over F₃₂	[i]
18	Digital (30, 36, large)-net over F₃₂	[i]
19	(29, 35, 349526)-net in base 8	[i]	Base Change