MinT - Best Known (77−58, 77, s)-Nets in Base 9

Best Known (77−58, 77, s)-Nets in Base 9

(77−58, 77, 74)-Net over F₉ — Constructive and digital

Digital (19, 77, 74)-net over F₉, using

t-expansion [i] based on digital (17, 77, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(77−58, 77, 84)-Net over F₉ — Digital

Digital (19, 77, 84)-net over F₉, using

net from sequence [i] based on digital (19, 83)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
  - Drinfeld modules of rank 1 [i]

(77−58, 77, 481)-Net in Base 9 — Upper bound on s

There is no (19, 77, 482)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 31 562067 372591 313033 988761 998072 663861 854851 625603 817800 213514 032324 283729 > 9⁷⁷ [i]