MinT - Best Known (56, 98, s)-Nets in Base 25

Best Known (56, 98, s)-Nets in Base 25

(56, 98, 326)-Net over F₂₅ — Constructive and digital

Digital (56, 98, 326)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 31, 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 (25, 67, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(56, 98, 1497)-Net over F₂₅ — Digital

Digital (56, 98, 1497)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 98, 1207806)-Net in Base 25 — Upper bound on s

There is no (56, 98, 1207807)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 99568 661575 445539 578511 840464 292991 151669 256922 213847 010248 874436 119313 283813 808132 348707 977327 640588 423152 132595 444504 041072 424927 694345 > 25⁹⁸ [i]