MinT - Best Known (68−40, 68, s)-Nets in Base 25

Best Known (68−40, 68, s)-Nets in Base 25

(68−40, 68, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 68, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 68, 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]

(68−40, 68, 19582)-Net in Base 25 — Upper bound on s

There is no (28, 68, 19583)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 114885 758270 381403 707476 503933 870269 550884 875564 003967 295617 077466 951045 492210 427570 634760 883745 > 25⁶⁸ [i]