MinT - Best Known (27, 61, s)-Nets in Base 25

Best Known (27, 61, s)-Nets in Base 25

(27, 61, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 61, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 61, 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]

(27, 61, 210)-Net over F₂₅ — Digital

Digital (27, 61, 210)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 61, 31027)-Net in Base 25 — Upper bound on s

There is no (27, 61, 31028)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 18 810857 400642 126110 415129 309133 110105 595808 735115 638030 090416 891397 975273 079475 556065 > 25⁶¹ [i]