MinT - Best Known (9, 9+51, s)-Nets in Base 25

Best Known (9, 9+51, s)-Nets in Base 25

(9, 9+51, 104)-Net over F₂₅ — Constructive and digital

Digital (9, 60, 104)-net over F₂₅, using

net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
  - a function field by GarcÃa and Quoos [i]

(9, 9+51, 831)-Net in Base 25 — Upper bound on s

There is no (9, 60, 832)-net in base 25, because

1 times m-reduction [i] would yield (9, 59, 832)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 30619 425029 837052 296718 573118 461156 837531 601912 963504 524945 886618 897416 629382 053377 > 25⁵⁹ [i]