MinT - Best Known (64−35, 64, s)-Nets in Base 25

Best Known (64−35, 64, s)-Nets in Base 25

(64−35, 64, 200)-Net over F₂₅ — Constructive and digital

Digital (29, 64, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 64, 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]

(64−35, 64, 243)-Net over F₂₅ — Digital

Digital (29, 64, 243)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−35, 64, 45316)-Net in Base 25 — Upper bound on s

There is no (29, 64, 45317)-net in base 25, because

1 times m-reduction [i] would yield (29, 63, 45317)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 11759 279863 663400 166976 253101 338457 294799 567065 936917 024654 098159 243157 833408 324506 476025 > 25⁶³ [i]