MinT - Best Known (104−82, 104, s)-Nets in Base 25

Best Known (104−82, 104, s)-Nets in Base 25

(104−82, 104, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 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]

(104−82, 104, 171)-Net over F₂₅ — Digital

Digital (22, 104, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 104, 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]

(104−82, 104, 2342)-Net in Base 25 — Upper bound on s

There is no (22, 104, 2343)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 24 478075 524848 716063 879020 244908 791767 942347 100552 738987 847773 870713 869812 348698 919782 910856 303653 587263 977636 899220 811797 698336 425927 363502 623209 > 25¹⁰⁴ [i]