MinT - Best Known (78−61, 78, s)-Nets in Base 9

Best Known (78−61, 78, s)-Nets in Base 9

(78−61, 78, 74)-Net over F₉ — Constructive and digital

Digital (17, 78, 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]

(78−61, 78, 405)-Net in Base 9 — Upper bound on s

There is no (17, 78, 406)-net in base 9, because

1 times m-reduction [i] would yield (17, 77, 406)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 30 950469 134822 109323 385016 996269 868938 185724 018682 269854 988539 610251 535969 > 9⁷⁷ [i]