MinT - Best Known (94, 94+45, s)-Nets in Base 9

Best Known (94, 94+45, s)-Nets in Base 9

(94, 94+45, 740)-Net over F₉ — Constructive and digital

Digital (94, 139, 740)-net over F₉, using

t-expansion [i] based on digital (91, 139, 740)-net over F₉, using
- 11 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(94, 94+45, 2252)-Net over F₉ — Digital

Digital (94, 139, 2252)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+45, 1095117)-Net in Base 9 — Upper bound on s

There is no (94, 139, 1095118)-net in base 9, because

1 times m-reduction [i] would yield (94, 138, 1095118)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 484695 405292 891628 482202 117380 118592 561497 949501 731595 015044 956612 045328 102650 512454 392882 965132 774990 980212 560623 072376 908207 904097 > 9¹³⁸ [i]