MinT - Best Known (59, 59+38, s)-Nets in Base 25

Best Known (59, 59+38, s)-Nets in Base 25

(59, 59+38, 334)-Net over F₂₅ — Constructive and digital

Digital (59, 97, 334)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (9, 21, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]
2. digital (9, 28, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅ (see above)
3. digital (10, 48, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(59, 59+38, 2841)-Net over F₂₅ — Digital

Digital (59, 97, 2841)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+38, 4527463)-Net in Base 25 — Upper bound on s

There is no (59, 97, 4527464)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3982 739725 253278 649550 231990 266554 831625 988558 983735 674772 907353 427856 698141 643587 577340 510055 156414 992741 589775 441055 617215 340681 564225 > 25⁹⁷ [i]