MinT - Best Known (23, 23+71, s)-Nets in Base 25

Best Known (23, 23+71, s)-Nets in Base 25

(23, 23+71, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 94, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 94, 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]

(23, 23+71, 176)-Net over F₂₅ — Digital

Digital (23, 94, 176)-net over F₂₅, using

net from sequence [i] based on digital (23, 175)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 23 and N(F) ≥ 176, using
  - an algebraic function field by Teo [i]

(23, 23+71, 2984)-Net in Base 25 — Upper bound on s

There is no (23, 94, 2985)-net in base 25, because

1 times m-reduction [i] would yield (23, 93, 2985)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10227 934270 944384 423296 140535 130035 362007 566865 780319 520692 576375 896076 715073 413651 943032 565528 188716 556124 707126 964482 436949 891145 > 25⁹³ [i]