MinT - Information on Result #1197144

Information on Result #1197144

Digital (63, 96, 977)-net over F₂₅, using net defined by OOA based on linear OOA(25⁹⁶, 977, F₂₅, 33, 33) (dual of [(977, 33), 32145, 34]-NRT-code), using

OOA 16-folding and stacking with additional row [i] based on linear OA(25⁹⁶, 15633, F₂₅, 33) (dual of [15633, 15537, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁹⁶, 15636, F₂₅, 33) (dual of [15636, 15540, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(29) [i] based on
    1. linear OA(25⁹⁴, 15625, F₂₅, 33) (dual of [15625, 15531, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(25⁸⁵, 15625, F₂₅, 30) (dual of [15625, 15540, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
    3. linear OA(25², 11, F₂₅, 2) (dual of [11, 9, 3]-code or 11-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		Method
1	Digital (64, 97, 977)-net over F₂₅	[i]	Net Duplication
2	Digital (65, 98, 977)-net over F₂₅	[i]
3	Digital (66, 99, 977)-net over F₂₅	[i]
4	Digital (63, 95, 977)-net over F₂₅	[i]	m-Reduction