MinT - Information on Result #1198716

Information on Result #1198716

Digital (9, 13, 524290)-net over F₃₂, using net defined by OOA based on linear OOA(32¹³, 524290, F₃₂, 4, 4) (dual of [(524290, 4), 2097147, 5]-NRT-code), using

OA 2-folding and stacking [i] based on linear OA(32¹³, 1048580, F₃₂, 4) (dual of [1048580, 1048567, 5]-code), using
- constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
  1. linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
  2. linear OA(32⁹, 1048576, F₃₂, 3) (dual of [1048576, 1048567, 4]-code or 1048576-cap in PG(8,32)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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 (11, 15, 524323)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
2	Digital (41, 49, 2621440)-net over F₃₂	[i]
3	Digital (45, 54, 2621440)-net over F₃₂	[i]
4	(40, 48, 2621440)-net in base 32	[i]
5	(44, 53, 2621440)-net in base 32	[i]
6	Digital (94, 107, 5592416)-net over F₃₂	[i]	Generalized (u,Â u+v)-Construction for Nets
7	Digital (95, 108, 5592448)-net over F₃₂	[i]
8	Digital (97, 110, 5592480)-net over F₃₂	[i]
9	Digital (90, 102, 5592416)-net over F₃₂	[i]
10	Digital (91, 103, 5592448)-net over F₃₂	[i]
11	Digital (92, 104, 5592480)-net over F₃₂	[i]
12	Digital (94, 106, 5592512)-net over F₃₂	[i]
13	Digital (95, 107, 5592544)-net over F₃₂	[i]
14	Digital (96, 108, 5593472)-net over F₃₂	[i]
15	Digital (97, 109, 5593824)-net over F₃₂	[i]
16	Digital (98, 110, 5593856)-net over F₃₂	[i]
17	Digital (54, 63, large)-net over F₃₂	[i]
18	Digital (48, 56, large)-net over F₃₂	[i]
19	Digital (16, 20, large)-net over F₃₂	[i]
20	Digital (92, 105, 3320556)-net over F₃₂	[i]
21	Digital (93, 106, 3321548)-net over F₃₂	[i]
22	Digital (88, 100, 3320556)-net over F₃₂	[i]
23	Digital (89, 101, 3321548)-net over F₃₂	[i]
24	Digital (90, 103, 3320523)-net over F₃₂	[i]
25	Digital (91, 104, 3321515)-net over F₃₂	[i]
26	Digital (92, 105, 3323626)-net over F₃₂	[i]
27	Digital (93, 106, 3355340)-net over F₃₂	[i]
28	Digital (86, 98, 3320523)-net over F₃₂	[i]
29	Digital (87, 99, 3321515)-net over F₃₂	[i]
30	Digital (88, 100, 3323626)-net over F₃₂	[i]
31	Digital (89, 101, 3355340)-net over F₃₂	[i]
32	Digital (96, 110, 2921032)-net over F₃₂	[i]
33	Digital (87, 100, 3320490)-net over F₃₂	[i]
34	Digital (83, 95, 3320490)-net over F₃₂	[i]