MinT - Information on Result #1179456

Information on Result #1179456

Digital (22, 26, 390629)-net over F₅, using net defined by OOA based on linear OOA(5²⁶, 390629, F₅, 4, 4) (dual of [(390629, 4), 1562490, 5]-NRT-code), using

appending kth column [i] based on linear OOA(5²⁶, 390629, F₅, 3, 4) (dual of [(390629, 3), 1171861, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(5²⁶, 781258, F₅, 4) (dual of [781258, 781232, 5]-code), using
  - trace code [i] based on linear OA(25¹³, 390629, F₂₅, 4) (dual of [390629, 390616, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(25¹³, 390625, F₂₅, 4) (dual of [390625, 390612, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(25⁹, 390625, F₂₅, 3) (dual of [390625, 390616, 4]-code or 390625-cap in PG(8,25)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(25⁰, 4, F₂₅, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 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 (23, 27, 390629)-net over F₅	[i]	Net Duplication
2	Digital (90, 98, 4584929)-net over F₅	[i]	(u,Â u+v)-Construction for Nets
3	Digital (99, 108, 4584929)-net over F₅	[i]	(u,Â u+v)-Construction for Nets