MinT - Best Known (45−31, 45, s)-Nets in Base 25

Best Known (45−31, 45, s)-Nets in Base 25

(45−31, 45, 126)-Net over F₂₅ — Constructive and digital

Digital (14, 45, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 45, 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]

(45−31, 45, 130)-Net over F₂₅ — Digital

Digital (14, 45, 130)-net over F₂₅, using

net from sequence [i] based on digital (14, 129)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 14 and N(F) ≥ 130, using
  - an algebraic function field by Teo [i]

(45−31, 45, 3366)-Net in Base 25 — Upper bound on s

There is no (14, 45, 3367)-net in base 25, because

1 times m-reduction [i] would yield (14, 44, 3367)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 32 362634 273738 122689 124728 674284 628089 696247 842746 230030 268889 > 25⁴⁴ [i]