MinT - Best Known (55, 55+38, s)-Nets in Base 25

Best Known (55, 55+38, s)-Nets in Base 25

(55, 55+38, 326)-Net over F₂₅ — Constructive and digital

Digital (55, 93, 326)-net over F₂₅, using

2 times m-reduction [i] based on digital (55, 95, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 30, 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, 65, 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]

(55, 55+38, 2011)-Net over F₂₅ — Digital

Digital (55, 93, 2011)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+38, 2299063)-Net in Base 25 — Upper bound on s

There is no (55, 93, 2299064)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10195 869659 695961 649020 249210 698819 055905 680819 873143 957254 028501 050608 789040 341313 135568 499504 537215 851772 418983 866804 090063 353025 > 25⁹³ [i]