MinT - Best Known (68, 68+42, s)-Nets in Base 9

Best Known (68, 68+42, s)-Nets in Base 9

(68, 68+42, 448)-Net over F₉ — Constructive and digital

Digital (68, 110, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 55, 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]

(68, 68+42, 753)-Net over F₉ — Digital

Digital (68, 110, 753)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+42, 108084)-Net in Base 9 — Upper bound on s

There is no (68, 110, 108085)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 926 157770 035892 435512 355998 897418 354671 965267 479489 449174 194502 128679 116194 984542 175485 263867 664572 724809 > 9¹¹⁰ [i]