MinT - Information on Result #1021038

Information on Result #1021038

Linear OOA(3¹⁵³, 64, F₃, 3, 77) (dual of [(64, 3), 39, 78]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3³⁶, 20, F₃, 3, 25) (dual of [(20, 3), 24, 26]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 36, 20)-net over F₃, using
  - net from sequence [i] based on digital (11, 19)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 9, N(F)Â =Â 19, and 1 place with degree 3 [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
linear OOA(3⁵¹, 22, F₃, 3, 38) (dual of [(22, 3), 15, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁵¹, 23, F₃, 3, 38) (dual of [(23, 3), 18, 39]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,30P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
linear OOA(3⁶⁶, 22, F₃, 3, 66) (dual of [(22, 3), 0, 67]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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