MinT - Best Known (73−45, 73, s)-Nets in Base 25

Best Known (73−45, 73, s)-Nets in Base 25

(73−45, 73, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 73, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 73, 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]

(73−45, 73, 14169)-Net in Base 25 — Upper bound on s

There is no (28, 73, 14170)-net in base 25, because

1 times m-reduction [i] would yield (28, 72, 14170)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 44844 674229 040822 852412 944687 903341 006477 809345 591093 678159 517355 411376 316579 260622 655315 322441 970145 > 25⁷² [i]