MinT - Best Known (23, 104, s)-Nets in Base 25

Best Known (23, 104, s)-Nets in Base 25

(23, 104, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 104, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 104, 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, 104, 176)-Net over F₂₅ — Digital

Digital (23, 104, 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, 104, 2592)-Net in Base 25 — Upper bound on s

There is no (23, 104, 2593)-net in base 25, because

1 times m-reduction [i] would yield (23, 103, 2593)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 976968 429366 318613 500551 771673 884054 532918 492378 635980 970919 604921 343421 725811 088444 290060 388568 704315 489272 410706 899353 221483 314000 003955 218113 > 25¹⁰³ [i]