MinT - Best Known (74, 74+44, s)-Nets in Base 9

Best Known (74, 74+44, s)-Nets in Base 9

Digital (74, 118, 448)-net over F₉, using

4 times m-reduction [i] based on digital (74, 122, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 61, 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 (74, 118, 899)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9¹¹⁸, 899, F₉, 44) (dual of [899, 781, 45]-code), using
- 780 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (7, 2, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 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, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 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, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0) [i] based on linear OA(9⁴⁴, 45, F₉, 44) (dual of [45, 1, 45]-code or 45-arc in PG(43,9)), using
  - dual of repetition code with length 45 [i]

There is no (74, 118, 148572)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39872 960607 276825 021238 968874 844078 222088 226705 305334 992555 325460 988087 375014 207839 456768 505334 424514 853139 127745 > 9¹¹⁸ [i]