MinT - Best Known (55, 55+30, s)-Nets in Base 9

Best Known (55, 55+30, s)-Nets in Base 9

Digital (55, 85, 344)-net over F₉, using

11 times m-reduction [i] based on digital (55, 96, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 48, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

Digital (55, 85, 929)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁸⁵, 929, F₉, 30) (dual of [929, 844, 31]-code), using
- 843 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (5, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 34 times 0, 1, 37 times 0, 1, 41 times 0, 1, 43 times 0, 1, 47 times 0, 1, 52 times 0, 1, 55 times 0, 1, 60 times 0, 1, 65 times 0) [i] based on linear OA(9³⁰, 31, F₉, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,9)), using
  - dual of repetition code with length 31 [i]

There is no (55, 85, 205132)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1290 129316 540955 378040 512530 234679 615646 631298 567507 632975 818056 024826 844006 890273 > 9⁸⁵ [i]