MinT - Best Known (83−63, 83, s)-Nets in Base 25

Best Known (83−63, 83, s)-Nets in Base 25

(83−63, 83, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 83, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 83, 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]

(83−63, 83, 171)-Net over F₂₅ — Digital

Digital (20, 83, 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]

(83−63, 83, 2563)-Net in Base 25 — Upper bound on s

There is no (20, 83, 2564)-net in base 25, because

1 times m-reduction [i] would yield (20, 82, 2564)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 296729 212092 258608 024781 503464 598359 247261 724805 863470 843171 688882 776015 698034 724539 710421 732750 330868 520031 040033 > 25⁸² [i]