MinT - Information on Result #1179646

Information on Result #1179646

Digital (9, 13, 2882402)-net over F₄₉, using net defined by OOA based on linear OOA(49¹³, 2882402, F₄₉, 4, 4) (dual of [(2882402, 4), 11529595, 5]-NRT-code), using

appending kth column [i] based on linear OOA(49¹³, 2882402, F₄₉, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(49¹³, 5764804, F₄₉, 4) (dual of [5764804, 5764791, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(49¹³, 5764805, F₄₉, 4) (dual of [5764805, 5764792, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(49⁹, 5764801, F₄₉, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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 (34, 42, 2882402)-net over F₄₉	[i]	(u,Â u+v)-Construction for Nets
2	Digital (35, 43, 2882404)-net over F₄₉	[i]
3	Digital (45, 53, 4194400)-net over F₄₉	[i]
4	Digital (46, 54, 4194402)-net over F₄₉	[i]
5	Digital (47, 55, 5764804)-net over F₄₉	[i]
6	Digital (37, 46, 2882402)-net over F₄₉	[i]
7	Digital (38, 47, 2882404)-net over F₄₉	[i]
8	Digital (39, 48, 2882406)-net over F₄₉	[i]
9	Digital (46, 54, large)-net over F₄₉	[i]	Generalized (u,Â u+v)-Construction for Nets
10	Digital (45, 53, 4325903)-net over F₄₉	[i]
11	Digital (44, 52, 4323803)-net over F₄₉	[i]
12	Digital (45, 53, 4333407)-net over F₄₉	[i]
13	Digital (43, 51, 4323753)-net over F₄₉	[i]
14	Digital (44, 52, 4330956)-net over F₄₉	[i]
15	Digital (45, 53, 4683903)-net over F₄₉	[i]
16	Digital (42, 50, 4323703)-net over F₄₉	[i]
17	Digital (43, 51, 4328505)-net over F₄₉	[i]
18	Digital (44, 52, 4563803)-net over F₄₉	[i]
19	Digital (45, 53, 7206005)-net over F₄₉	[i]
20	Digital (46, 55, 4323653)-net over F₄₉	[i]
21	Digital (41, 49, 4323653)-net over F₄₉	[i]
22	Digital (42, 50, 4326054)-net over F₄₉	[i]
23	Digital (43, 51, 4443703)-net over F₄₉	[i]
24	Digital (44, 52, 5764804)-net over F₄₉	[i]
25	Digital (40, 49, 2882452)-net over F₄₉	[i]
26	Digital (41, 50, 2884804)-net over F₄₉	[i]
27	Digital (42, 51, 2888352)-net over F₄₉	[i]
28	Digital (43, 52, 3002602)-net over F₄₉	[i]
29	Digital (44, 53, 4323603)-net over F₄₉	[i]
30	Digital (45, 54, 4323606)-net over F₄₉	[i]
31	Digital (36, 44, 2882452)-net over F₄₉	[i]
32	Digital (37, 45, 2884853)-net over F₄₉	[i]
33	Digital (38, 46, 3002502)-net over F₄₉	[i]
34	Digital (39, 47, 4323603)-net over F₄₉	[i]
35	Digital (40, 48, 4323606)-net over F₄₉	[i]