MinT - Best Known (110−88, 110, s)-Nets in Base 25

Best Known (110−88, 110, s)-Nets in Base 25

(110−88, 110, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 110, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 110, 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]

(110−88, 110, 171)-Net over F₂₅ — Digital

Digital (22, 110, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 110, 171)-net over F₂₅, using
- net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
    - an algebraic function field by Teo [i]

(110−88, 110, 2223)-Net in Base 25 — Upper bound on s

There is no (22, 110, 2224)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 5992 466600 380810 213711 172633 142940 329550 186225 210779 793984 972028 650097 076157 007028 528492 464511 094349 730406 749736 829132 223010 245950 306663 478661 342856 446465 > 25¹¹⁰ [i]