MinT - Best Known (19, 19+65, s)-Nets in Base 9

Best Known (19, 19+65, s)-Nets in Base 9

(19, 19+65, 74)-Net over F₉ — Constructive and digital

Digital (19, 84, 74)-net over F₉, using

t-expansion [i] based on digital (17, 84, 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]

(19, 19+65, 84)-Net over F₉ — Digital

Digital (19, 84, 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]

(19, 19+65, 458)-Net in Base 9 — Upper bound on s

There is no (19, 84, 459)-net in base 9, because

1 times m-reduction [i] would yield (19, 83, 459)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 16 912627 108008 754298 789255 416759 950131 789588 881607 062875 786695 380495 312070 066945 > 9⁸³ [i]