MinT - Best Known (95−71, 95, s)-Nets in Base 25

Best Known (95−71, 95, s)-Nets in Base 25

(95−71, 95, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 95, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 95, 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]

(95−71, 95, 184)-Net over F₂₅ — Digital

Digital (24, 95, 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]

(95−71, 95, 3274)-Net in Base 25 — Upper bound on s

There is no (24, 95, 3275)-net in base 25, because

1 times m-reduction [i] would yield (24, 94, 3275)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 257560 554419 098320 492798 003144 112715 107097 585894 211228 554803 215225 782627 324668 840499 935916 088518 636306 696691 486519 718464 882275 560345 > 25⁹⁴ [i]