MinT - Best Known (69−45, 69, s)-Nets in Base 25

Best Known (69−45, 69, s)-Nets in Base 25

(69−45, 69, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 69, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 69, 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]

(69−45, 69, 184)-Net over F₂₅ — Digital

Digital (24, 69, 184)-net over F₂₅, using

net from sequence [i] based on digital (24, 183)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 24 and N(F) ≥ 184, using
  - an algebraic function field by Teo [i]

(69−45, 69, 7887)-Net in Base 25 — Upper bound on s

There is no (24, 69, 7888)-net in base 25, because

1 times m-reduction [i] would yield (24, 68, 7888)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 115071 186973 515042 354195 259505 640408 361863 294718 415433 554850 602779 307231 195783 449063 306825 569025 > 25⁶⁸ [i]