MinT - Information on Result #1012929

Information on Result #1012929

Linear OOA(5¹⁸, 62, F₅, 3, 7) (dual of [(62, 3), 168, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5⁵, 66, F₅, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
    - caps completed using a computer search [i]
linear OOA(5¹³, 31, F₅, 3, 7) (dual of [(31, 3), 80, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5³, 6, F₅, 3, 3) (dual of [(6, 3), 15, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;15,5) [i]
  2. 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]

Mode: Constructive and linear.

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