MinT - Best Known (59, 59+39, s)-Nets in Base 25

Best Known (59, 59+39, s)-Nets in Base 25

(59, 59+39, 330)-Net over F₂₅ — Constructive and digital

Digital (59, 98, 330)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 29, 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]
2. digital (30, 69, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(59, 59+39, 2541)-Net over F₂₅ — Digital

Digital (59, 98, 2541)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+39, 4527463)-Net in Base 25 — Upper bound on s

There is no (59, 98, 4527464)-net in base 25, because

1 times m-reduction [i] would yield (59, 97, 4527464)-net in base 25, but
- 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]