MinT - Best Known (105−41, 105, s)-Nets in Base 9

Best Known (105−41, 105, s)-Nets in Base 9

(105−41, 105, 344)-Net over F₉ — Constructive and digital

Digital (64, 105, 344)-net over F₉, using

9 times m-reduction [i] based on digital (64, 114, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 57, 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]

(105−41, 105, 650)-Net over F₉ — Digital

Digital (64, 105, 650)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−41, 105, 95109)-Net in Base 9 — Upper bound on s

There is no (64, 105, 95110)-net in base 9, because

1 times m-reduction [i] would yield (64, 104, 95110)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1742 988580 619606 114843 774386 601032 007629 154423 045097 458817 737240 456282 832001 973752 933757 143195 834689 > 9¹⁰⁴ [i]