MinT - Best Known (17, 17+77, s)-Nets in Base 25

Best Known (17, 17+77, s)-Nets in Base 25

(17, 17+77, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 94, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 94, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(17, 17+77, 150)-Net over F₂₅ — Digital

Digital (17, 94, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 94, 150)-net over F₂₅, using
- net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
    - an algebraic function field by Teo [i]

(17, 17+77, 1631)-Net in Base 25 — Upper bound on s

There is no (17, 94, 1632)-net in base 25, because

1 times m-reduction [i] would yield (17, 93, 1632)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10331 757024 343622 078569 406240 978966 366510 742351 178242 476103 785745 946923 231865 512246 284359 565121 272260 561830 705391 593783 432391 002625 > 25⁹³ [i]