MinT - Best Known (67, 67+41, s)-Nets in Base 9

Best Known (67, 67+41, s)-Nets in Base 9

(67, 67+41, 448)-Net over F₉ — Constructive and digital

Digital (67, 108, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 54, 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]

(67, 67+41, 763)-Net over F₉ — Digital

Digital (67, 108, 763)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+41, 132243)-Net in Base 9 — Upper bound on s

There is no (67, 108, 132244)-net in base 9, because

1 times m-reduction [i] would yield (67, 107, 132244)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 270523 708188 303365 837298 223154 589115 410169 589464 338757 893320 613961 824084 591762 085066 359248 743968 408449 > 9¹⁰⁷ [i]