MinT - Best Known (67, 105, s)-Nets in Base 9

Best Known (67, 105, s)-Nets in Base 9

Digital (67, 105, 448)-net over F₉, using

3 times m-reduction [i] based on digital (67, 108, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 54, 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 (67, 105, 954)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9¹⁰⁵, 954, F₉, 38) (dual of [954, 849, 39]-code), using
- 848 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 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, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 38 times 0, 1, 41 times 0, 1, 43 times 0, 1, 46 times 0, 1, 49 times 0, 1, 52 times 0) [i] based on linear OA(9³⁸, 39, F₉, 38) (dual of [39, 1, 39]-code or 39-arc in PG(37,9)), using
  - dual of repetition code with length 39 [i]

There is no (67, 105, 186014)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15685 078888 453813 655463 953401 332116 686824 217399 837048 957897 851421 550927 166060 299607 021939 422898 160785 > 9¹⁰⁵ [i]