MinT - Best Known (96−41, 96, s)-Nets in Base 9

Best Known (96−41, 96, s)-Nets in Base 9

(96−41, 96, 344)-Net over F₉ — Constructive and digital

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]

(96−41, 96, 387)-Net over F₉ — Digital

Digital (55, 96, 387)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−41, 96, 35376)-Net in Base 9 — Upper bound on s

There is no (55, 96, 35377)-net in base 9, because

1 times m-reduction [i] would yield (55, 95, 35377)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 498219 441018 802239 158379 088187 352541 194528 296945 650446 885549 486074 729013 759645 923982 238241 > 9⁹⁵ [i]