MinT - Best Known (65−45, 65, s)-Nets in Base 25

Best Known (65−45, 65, s)-Nets in Base 25

(65−45, 65, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 65, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 65, 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]

(65−45, 65, 171)-Net over F₂₅ — Digital

Digital (20, 65, 171)-net over F₂₅, using

net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
  - an algebraic function field by Teo [i]

(65−45, 65, 4387)-Net in Base 25 — Upper bound on s

There is no (20, 65, 4388)-net in base 25, because

1 times m-reduction [i] would yield (20, 64, 4388)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 294142 619543 826066 932974 191587 432423 438286 382107 298720 473581 209531 222488 220945 054606 578625 > 25⁶⁴ [i]