MinT - Best Known (24, 24+65, s)-Nets in Base 25

Best Known (24, 24+65, s)-Nets in Base 25

(24, 24+65, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 89, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 89, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(24, 24+65, 184)-Net over F₂₅ — Digital

Digital (24, 89, 184)-net over F₂₅, using

net from sequence [i] based on digital (24, 183)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 24 and N(F) ≥ 184, using
  - an algebraic function field by Teo [i]

(24, 24+65, 3707)-Net in Base 25 — Upper bound on s

There is no (24, 89, 3708)-net in base 25, because

1 times m-reduction [i] would yield (24, 88, 3708)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1051 823414 911501 979838 511745 497608 194979 704148 945050 531610 517462 776073 234841 850337 002162 352214 549677 167713 746095 308978 199553 > 25⁸⁸ [i]