MinT - Information on Result #1189550

Information on Result #1189550

Digital (100, 127, 1202)-net over F₅, using net defined by OOA based on linear OOA(5¹²⁷, 1202, F₅, 27, 27) (dual of [(1202, 27), 32327, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(5¹²⁷, 15627, F₅, 27) (dual of [15627, 15500, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹²⁷, 15631, F₅, 27) (dual of [15631, 15504, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
    1. linear OA(5¹²⁷, 15625, F₅, 27) (dual of [15625, 15498, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(5¹²¹, 15625, F₅, 26) (dual of [15625, 15504, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    3. linear OA(5⁰, 6, F₅, 0) (dual of [6, 6, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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 (101, 128, 1202)-net over F₅	[i]	Net Duplication
2	Digital (102, 129, 1202)-net over F₅	[i]	Net Duplication
3	Digital (113, 140, 1208)-net over F₅	[i]	(u,Â u+v)-Construction for Nets
4	Digital (114, 141, 1212)-net over F₅	[i]
5	Digital (115, 142, 1214)-net over F₅	[i]
6	Digital (116, 143, 1218)-net over F₅	[i]
7	Digital (117, 144, 1220)-net over F₅	[i]
8	Digital (118, 145, 1222)-net over F₅	[i]
9	Digital (119, 146, 1223)-net over F₅	[i]
10	Digital (120, 147, 1224)-net over F₅	[i]