MinT - Best Known (85−61, 85, s)-Nets in Base 25

Best Known (85−61, 85, s)-Nets in Base 25

(85−61, 85, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 85, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 85, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(85−61, 85, 184)-Net over F₂₅ — Digital

Digital (24, 85, 184)-net over F₂₅, using

net from sequence [i] based on digital (24, 183)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 24 and N(F) ≥ 184, using
  - an algebraic function field by Teo [i]

(85−61, 85, 4103)-Net in Base 25 — Upper bound on s

There is no (24, 85, 4104)-net in base 25, because

1 times m-reduction [i] would yield (24, 84, 4104)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2683 859864 138269 879229 889975 048893 907355 373216 417489 323975 822213 787562 838314 702175 372188 246263 656684 860834 310460 774785 > 25⁸⁴ [i]