MinT - Information on Result #1213652

Information on Result #1213652

Digital (92, 107, 55829)-net over F₅, using (u,Â u+v)-construction based on

digital (3, 10, 25)-net over F₅, using
- linear code embedding found in a computer search [i]
digital (82, 97, 55804)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁹⁷, 55804, F₅, 15, 15) (dual of [(55804, 15), 836963, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(5⁹⁷, 390629, F₅, 15) (dual of [390629, 390532, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁹⁷, 390633, F₅, 15) (dual of [390633, 390536, 16]-code), using
      - 1 times truncation [i] based on linear OA(5⁹⁸, 390634, F₅, 16) (dual of [390634, 390536, 17]-code), using
        constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
        linear OA(5⁹⁷, 390625, F₅, 16) (dual of [390625, 390528, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(5⁸⁹, 390625, F₅, 14) (dual of [390625, 390536, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(5¹, 9, F₅, 1) (dual of [9, 8, 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

None.