MinT - Best Known (62−45, 62, s)-Nets in Base 9

Best Known (62−45, 62, s)-Nets in Base 9

(62−45, 62, 74)-Net over F₉ — Constructive and digital

Digital (17, 62, 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]

(62−45, 62, 487)-Net in Base 9 — Upper bound on s

There is no (17, 62, 488)-net in base 9, because

1 times m-reduction [i] would yield (17, 61, 488)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 16459 948385 856739 577925 620189 604405 634642 653798 223042 343553 > 9⁶¹ [i]