MinT - Best Known (50, 50+22, s)-Nets in Base 9

Best Known (50, 50+22, s)-Nets in Base 9

Digital (50, 72, 448)-net over F₉, using

2 times m-reduction [i] based on digital (50, 74, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 37, 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 (50, 72, 2039)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁷², 2039, F₉, 22) (dual of [2039, 1967, 23]-code), using
- 1966 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 29 times 0, 1, 32 times 0, 1, 36 times 0, 1, 40 times 0, 1, 44 times 0, 1, 50 times 0, 1, 55 times 0, 1, 62 times 0, 1, 69 times 0, 1, 76 times 0, 1, 86 times 0, 1, 95 times 0, 1, 105 times 0, 1, 117 times 0, 1, 131 times 0, 1, 145 times 0, 1, 162 times 0, 1, 179 times 0, 1, 200 times 0) [i] based on linear OA(9²², 23, F₉, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,9)), using
  - dual of repetition code with length 23 [i]

There is no (50, 72, 1081117)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 507 530293 550024 521642 328831 255070 641266 019854 715226 060242 144349 504825 > 9⁷² [i]