MinT - Best Known (23, 80, s)-Nets in Base 25

Best Known (23, 80, s)-Nets in Base 25

(23, 80, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 80, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 80, 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, 80, 176)-Net over F₂₅ — Digital

Digital (23, 80, 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, 80, 4125)-Net in Base 25 — Upper bound on s

There is no (23, 80, 4126)-net in base 25, because

1 times m-reduction [i] would yield (23, 79, 4126)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 275 236965 747196 360177 132324 669001 243389 306944 578759 362377 430577 579167 567396 716867 527437 028966 405751 924148 578625 > 25⁷⁹ [i]