MinT - Information on Result #1189290

Information on Result #1189290

Digital (117, 136, 217014)-net over F₅, using net defined by OOA based on linear OOA(5¹³⁶, 217014, F₅, 19, 19) (dual of [(217014, 19), 4123130, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(5¹³⁶, 1953127, F₅, 19) (dual of [1953127, 1952991, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹³⁶, 1953134, F₅, 19) (dual of [1953134, 1952998, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
    1. linear OA(5¹³⁶, 1953125, F₅, 19) (dual of [1953125, 1952989, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(5¹²⁷, 1953125, F₅, 18) (dual of [1953125, 1952998, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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 (126, 145, 217020)-net over F₅	[i]	(u,Â u+v)-Construction for Nets
2	Digital (127, 146, 217024)-net over F₅	[i]
3	Digital (128, 147, 217026)-net over F₅	[i]
4	Digital (129, 148, 217030)-net over F₅	[i]
5	Digital (130, 149, 217032)-net over F₅	[i]
6	Digital (131, 150, 217034)-net over F₅	[i]