MinT - Best Known (51−35, 51, s)-Nets in Base 25

Best Known (51−35, 51, s)-Nets in Base 25

(51−35, 51, 126)-Net over F₂₅ — Constructive and digital

Digital (16, 51, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 51, 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]

(51−35, 51, 150)-Net over F₂₅ — Digital

Digital (16, 51, 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]

(51−35, 51, 3857)-Net in Base 25 — Upper bound on s

There is no (16, 51, 3858)-net in base 25, because

1 times m-reduction [i] would yield (16, 50, 3858)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 7894 375901 405520 225772 850242 944418 473838 793727 878815 922527 030481 709745 > 25⁵⁰ [i]