MinT - Best Known (68−47, 68, s)-Nets in Base 25

Best Known (68−47, 68, s)-Nets in Base 25

(68−47, 68, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 68, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 68, 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]

(68−47, 68, 171)-Net over F₂₅ — Digital

Digital (21, 68, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 68, 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]

(68−47, 68, 4627)-Net in Base 25 — Upper bound on s

There is no (21, 68, 4628)-net in base 25, because

1 times m-reduction [i] would yield (21, 67, 4628)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4593 806432 829620 753502 320566 097191 545898 862079 503424 095514 917934 501904 803598 858477 725302 622625 > 25⁶⁷ [i]