MinT - Best Known (67−45, 67, s)-Nets in Base 25

Best Known (67−45, 67, s)-Nets in Base 25

(67−45, 67, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 67, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 67, 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]

(67−45, 67, 171)-Net over F₂₅ — Digital

Digital (22, 67, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 67, 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]

(67−45, 67, 5883)-Net in Base 25 — Upper bound on s

There is no (22, 67, 5884)-net in base 25, because

1 times m-reduction [i] would yield (22, 66, 5884)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 184 158406 005425 496021 061953 319039 688713 093943 468737 878771 318743 291386 785834 169105 718286 517825 > 25⁶⁶ [i]