MinT - Information on Result #1179462

Information on Result #1179462

Digital (26, 30, 976573)-net over F₅, using net defined by OOA based on linear OOA(5³⁰, 976573, F₅, 4, 4) (dual of [(976573, 4), 3906262, 5]-NRT-code), using

appending kth column [i] based on linear OOA(5³⁰, 976573, F₅, 3, 4) (dual of [(976573, 3), 2929689, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(5³⁰, 1953146, F₅, 4) (dual of [1953146, 1953116, 5]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(5²⁹, 1953145, F₅, 4) (dual of [1953145, 1953116, 5]-code), using
    - constructionÂ X4 applied to C_e(3) âŠ‚ C_e(1) [i] based on
      1. linear OA(5²⁸, 1953125, F₅, 4) (dual of [1953125, 1953097, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(5¹⁰, 1953125, F₅, 2) (dual of [1953125, 1953115, 3]-code), using an extension C_e(1) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [i]
      3. linear OA(5¹⁹, 20, F₅, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
        dual of repetition code with length 20 [i]
      4. linear OA(5¹, 20, F₅, 1) (dual of [20, 19, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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		This result only	Method
1	Digital (94, 102, 5170873)-net over F₅	[i]		(u,Â u+v)-Construction for Nets
2	Digital (103, 112, 5170873)-net over F₅	[i]		(u,Â u+v)-Construction for Nets