MinT - Best Known (102−79, 102, s)-Nets in Base 25

Best Known (102−79, 102, s)-Nets in Base 25

(102−79, 102, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 102, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 102, 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]

(102−79, 102, 176)-Net over F₂₅ — Digital

Digital (23, 102, 176)-net over F₂₅, using

net from sequence [i] based on digital (23, 175)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 23 and N(F) ≥ 176, using
  - an algebraic function field by Teo [i]

(102−79, 102, 2655)-Net in Base 25 — Upper bound on s

There is no (23, 102, 2656)-net in base 25, because

1 times m-reduction [i] would yield (23, 101, 2656)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1564 377745 635150 792513 663006 332177 046855 114699 463637 127621 430017 470296 698948 069572 882764 984309 690205 698486 203039 184707 744949 600682 754020 346625 > 25¹⁰¹ [i]