MinT - Best Known (59, 90, s)-Nets in Base 9

Best Known (59, 90, s)-Nets in Base 9

Digital (59, 90, 448)-net over F₉, using

2 times m-reduction [i] based on digital (59, 92, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 46, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

Digital (59, 90, 1113)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁹⁰, 1113, F₉, 31) (dual of [1113, 1023, 32]-code), using
- 1022 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (5, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 48 times 0, 1, 52 times 0, 1, 56 times 0, 1, 60 times 0, 1, 65 times 0, 1, 70 times 0, 1, 76 times 0) [i] based on linear OA(9³¹, 32, F₉, 31) (dual of [32, 1, 32]-code or 32-arc in PG(30,9)), using
  - dual of repetition code with length 32 [i]

There is no (59, 90, 368558)-net in base 9, because

1 times m-reduction [i] would yield (59, 89, 368558)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 464371 144421 627417 444197 803325 087769 046715 036001 637918 172055 211324 778115 090735 792593 > 9⁸⁹ [i]