MinT - Information on Result #1189128

Information on Result #1189128

Digital (101, 118, 244141)-net over F₅, using net defined by OOA based on linear OOA(5¹¹⁸, 244141, F₅, 17, 17) (dual of [(244141, 17), 4150279, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(5¹¹⁸, 1953129, F₅, 17) (dual of [1953129, 1953011, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹¹⁸, 1953134, F₅, 17) (dual of [1953134, 1953016, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
    1. linear OA(5¹¹⁸, 1953125, F₅, 17) (dual of [1953125, 1953007, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(5¹⁰⁹, 1953125, F₅, 16) (dual of [1953125, 1953016, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(5⁰, 9, F₅, 0) (dual of [9, 9, 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 (102, 119, 244141)-net over F₅	[i]	Net Duplication
2	Digital (103, 120, 244141)-net over F₅	[i]	Net Duplication
3	Digital (109, 126, 244147)-net over F₅	[i]	(u,Â u+v)-Construction for Nets
4	Digital (110, 127, 244151)-net over F₅	[i]
5	Digital (111, 128, 244153)-net over F₅	[i]
6	Digital (112, 129, 244157)-net over F₅	[i]
7	Digital (113, 130, 244159)-net over F₅	[i]