MinT - Best Known (67−47, 67, s)-Nets in Base 25

Best Known (67−47, 67, s)-Nets in Base 25

(67−47, 67, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 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]

(67−47, 67, 171)-Net over F₂₅ — Digital

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]

(67−47, 67, 4021)-Net in Base 25 — Upper bound on s

There is no (20, 67, 4022)-net in base 25, because

1 times m-reduction [i] would yield (20, 66, 4022)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 183 724166 014409 933323 150617 499066 758774 190520 105462 885260 677836 643723 983552 773544 583792 744625 > 25⁶⁶ [i]