MinT - Best Known (78−55, 78, s)-Nets in Base 25

Best Known (78−55, 78, s)-Nets in Base 25

(78−55, 78, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 78, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 78, 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]

(78−55, 78, 176)-Net over F₂₅ — Digital

Digital (23, 78, 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]

(78−55, 78, 4400)-Net in Base 25 — Upper bound on s

There is no (23, 78, 4401)-net in base 25, because

1 times m-reduction [i] would yield (23, 77, 4401)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 438686 675968 942798 913579 690285 475027 765852 519219 184227 727517 804228 726841 424956 104681 401126 433764 383665 415625 > 25⁷⁷ [i]