MinT - Best Known (35, 60, s)-Nets in Base 25

Best Known (35, 60, s)-Nets in Base 25

(35, 60, 252)-Net over F₂₅ — Constructive and digital

Digital (35, 60, 252)-net over F₂₅, using

5 times m-reduction [i] based on digital (35, 65, 252)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 25, 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 (10, 40, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(35, 60, 1288)-Net over F₂₅ — Digital

Digital (35, 60, 1288)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(35, 60, 1645711)-Net in Base 25 — Upper bound on s

There is no (35, 60, 1645712)-net in base 25, because

1 times m-reduction [i] would yield (35, 59, 1645712)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 30092 825545 680663 215514 439291 783872 796186 856347 277018 686641 180354 490882 242500 519425 > 25⁵⁹ [i]