MinT - Best Known (100−77, 100, s)-Nets in Base 25

Best Known (100−77, 100, s)-Nets in Base 25

(100−77, 100, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 100, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 100, 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]

(100−77, 100, 176)-Net over F₂₅ — Digital

Digital (23, 100, 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]

(100−77, 100, 2725)-Net in Base 25 — Upper bound on s

There is no (23, 100, 2726)-net in base 25, because

1 times m-reduction [i] would yield (23, 99, 2726)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 514373 187354 049609 688480 002438 162454 743210 756277 331152 961866 211022 499589 405347 547077 823370 737049 834314 022733 345239 737183 938455 909707 656225 > 25⁹⁹ [i]