MinT - Best Known (94−35, 94, s)-Nets in Base 9

Best Known (94−35, 94, s)-Nets in Base 9

(94−35, 94, 344)-Net over F₉ — Constructive and digital

Digital (59, 94, 344)-net over F₉, using

10 times m-reduction [i] based on digital (59, 104, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 52, 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]

(94−35, 94, 752)-Net over F₉ — Digital

Digital (59, 94, 752)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−35, 94, 148968)-Net in Base 9 — Upper bound on s

There is no (59, 94, 148969)-net in base 9, because

1 times m-reduction [i] would yield (59, 93, 148969)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55538 402010 819631 059583 169333 373866 011148 992655 960311 012445 425144 966818 692745 814997 962185 > 9⁹³ [i]