MinT - Best Known (100−83, 100, s)-Nets in Base 9

Best Known (100−83, 100, s)-Nets in Base 9

(100−83, 100, 74)-Net over F₉ — Constructive and digital

Digital (17, 100, 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]

(100−83, 100, 381)-Net in Base 9 — Upper bound on s

There is no (17, 100, 382)-net in base 9, because

1 times m-reduction [i] would yield (17, 99, 382)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 30313 014130 212482 971221 277537 430913 735334 068574 724154 251817 986563 047806 507964 769971 799293 523569 > 9⁹⁹ [i]