MinT - Best Known (67−40, 67, s)-Nets in Base 25

Best Known (67−40, 67, s)-Nets in Base 25

(67−40, 67, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 67, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 67, 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]

(67−40, 67, 16669)-Net in Base 25 — Upper bound on s

There is no (27, 67, 16670)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4594 031241 250017 021639 860530 252946 809899 919549 693458 599052 549555 141020 738157 897487 033881 975745 > 25⁶⁷ [i]