MinT - Best Known (63, 112, s)-Nets in Base 9

Best Known (63, 112, s)-Nets in Base 9

(63, 112, 344)-Net over F₉ — Constructive and digital

Digital (63, 112, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 56, 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]

(63, 112, 389)-Net over F₉ — Digital

Digital (63, 112, 389)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 112, 31728)-Net in Base 9 — Upper bound on s

There is no (63, 112, 31729)-net in base 9, because

1 times m-reduction [i] would yield (63, 111, 31729)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8340 052888 457767 012192 878741 612309 253546 372679 456607 020882 025282 283170 458891 671796 023656 274729 063730 852289 > 9¹¹¹ [i]