MinT - Best Known (21, 21+59, s)-Nets in Base 25

Best Known (21, 21+59, s)-Nets in Base 25

(21, 21+59, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 80, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 80, 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]

(21, 21+59, 171)-Net over F₂₅ — Digital

Digital (21, 80, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 80, 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]

(21, 21+59, 3111)-Net in Base 25 — Upper bound on s

There is no (21, 80, 3112)-net in base 25, because

1 times m-reduction [i] would yield (21, 79, 3112)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 274 831885 410787 453130 942089 913414 907525 054742 468161 813324 304887 708455 403686 688344 743692 243070 474491 865184 819905 > 25⁷⁹ [i]