MinT - Information on Result #1198994

Information on Result #1198994

Digital (9, 19, 205)-net over F₃₂, using net defined by OOA based on linear OOA(32¹⁹, 205, F₃₂, 10, 10) (dual of [(205, 10), 2031, 11]-NRT-code), using

OA 5-folding and stacking [i] based on linear OA(32¹⁹, 1025, F₃₂, 10) (dual of [1025, 1006, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(32¹⁹, 1026, F₃₂, 10) (dual of [1026, 1007, 11]-code), using
  - constructionÂ X applied to C_e(9) âŠ‚ C_e(8) [i] based on
    1. linear OA(32¹⁹, 1024, F₃₂, 10) (dual of [1024, 1005, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    2. linear OA(32¹⁷, 1024, F₃₂, 9) (dual of [1024, 1007, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    3. 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]

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 (14, 24, 238)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
2	Digital (15, 25, 249)-net over F₃₂	[i]
3	Digital (16, 26, 410)-net over F₃₂	[i]
4	Digital (28, 48, 208)-net over F₃₂	[i]
5	Digital (30, 50, 240)-net over F₃₂	[i]
6	Digital (35, 55, 256)-net over F₃₂	[i]
7	Digital (36, 56, 262)-net over F₃₂	[i]
8	Digital (37, 57, 284)-net over F₃₂	[i]
9	Digital (28, 49, 208)-net over F₃₂	[i]
10	Digital (30, 51, 240)-net over F₃₂	[i]
11	Digital (35, 56, 256)-net over F₃₂	[i]
12	Digital (36, 57, 262)-net over F₃₂	[i]
13	Digital (37, 58, 284)-net over F₃₂	[i]
14	Digital (39, 60, 324)-net over F₃₂	[i]
15	Digital (59, 80, 3482)-net over F₃₂	[i]
16	Digital (79, 100, 105062)-net over F₃₂	[i]
17	Digital (57, 89, 360)-net over F₃₂	[i]	Generalized (u,Â u+v)-Construction for Nets