MinT - Best Known (79−26, 79, s)-Nets in Base 9

Best Known (79−26, 79, s)-Nets in Base 9

Digital (53, 79, 448)-net over F₉, using

1 times m-reduction [i] based on digital (53, 80, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 40, 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 (53, 79, 1331)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁷⁹, 1331, F₉, 26) (dual of [1331, 1252, 27]-code), using
- 1251 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 25 times 0, 1, 28 times 0, 1, 31 times 0, 1, 33 times 0, 1, 37 times 0, 1, 40 times 0, 1, 44 times 0, 1, 48 times 0, 1, 53 times 0, 1, 58 times 0, 1, 63 times 0, 1, 70 times 0, 1, 76 times 0, 1, 83 times 0, 1, 91 times 0, 1, 100 times 0, 1, 109 times 0) [i] based on linear OA(9²⁶, 27, F₉, 26) (dual of [27, 1, 27]-code or 27-arc in PG(25,9)), using
  - dual of repetition code with length 27 [i]

There is no (53, 79, 445828)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2427 512652 539494 505580 404404 471384 980016 980248 200154 717272 966551 488716 447905 > 9⁷⁹ [i]