MinT - Information on Result #1196674

Information on Result #1196674

Digital (56, 75, 43404)-net over F₂₅, using net defined by OOA based on linear OOA(25⁷⁵, 43404, F₂₅, 19, 19) (dual of [(43404, 19), 824601, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(25⁷⁵, 390637, F₂₅, 19) (dual of [390637, 390562, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁷⁵, 390639, F₂₅, 19) (dual of [390639, 390564, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
    1. linear OA(25⁷³, 390625, F₂₅, 19) (dual of [390625, 390552, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(25⁶¹, 390625, F₂₅, 16) (dual of [390625, 390564, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(25², 14, F₂₅, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,25)), using
      - discarding factors / shortening the dual code based on linear OA(25², 25, F₂₅, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
        Reedâ€“Solomon code RS(23,25) [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 (57, 76, 43404)-net over F₂₅	[i]		Net Duplication
2	Digital (69, 88, 43470)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets