MinT - Best Known (99−79, 99, s)-Nets in Base 9

Best Known (99−79, 99, s)-Nets in Base 9

(99−79, 99, 74)-Net over F₉ — Constructive and digital

Digital (20, 99, 74)-net over F₉, using

t-expansion [i] based on digital (17, 99, 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]

(99−79, 99, 84)-Net over F₉ — Digital

Digital (20, 99, 84)-net over F₉, using

t-expansion [i] based on digital (19, 99, 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]

(99−79, 99, 457)-Net in Base 9 — Upper bound on s

There is no (20, 99, 458)-net in base 9, because

1 times m-reduction [i] would yield (20, 98, 458)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3414 803579 902054 987667 506554 699823 679509 524172 873448 155409 945629 898022 258100 611563 158696 405745 > 9⁹⁸ [i]