MinT - Information on Result #1213614

Information on Result #1213614

Digital (113, 127, 1198426)-net over F₅, using (u,Â u+v)-construction based on

digital (9, 16, 55)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹⁶, 55, F₅, 9, 7) (dual of [(55, 9), 479, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(5¹⁶, 56, F₅, 3, 7) (dual of [(56, 3), 152, 8]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(5², 6, F₅, 3, 2) (dual of [(6, 3), 16, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;16,5) [i]
      2. linear OOA(5⁴, 25, F₅, 3, 3) (dual of [(25, 3), 71, 4]-NRT-code), using
        OOA stacking with additional row [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
      3. linear OOA(5¹⁰, 25, F₅, 3, 7) (dual of [(25, 3), 65, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, using
        linear code embedding found in a computer search [i]
digital (97, 111, 1198371)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹¹¹, 1198371, F₅, 14, 14) (dual of [(1198371, 14), 16777083, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(5¹¹¹, 8388597, F₅, 14) (dual of [8388597, 8388486, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹¹¹, large, F₅, 14) (dual of [large, large−111, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.