MinT - Best Known (108−87, 108, s)-Nets in Base 25

Best Known (108−87, 108, s)-Nets in Base 25

(108−87, 108, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 108, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 108, 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]

(108−87, 108, 171)-Net over F₂₅ — Digital

Digital (21, 108, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 108, 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]

(108−87, 108, 2094)-Net in Base 25 — Upper bound on s

There is no (21, 108, 2095)-net in base 25, because

1 times m-reduction [i] would yield (21, 107, 2095)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 380568 766044 307022 126009 392786 657313 020556 215897 043346 765249 822788 247414 802620 461789 255958 960404 339790 976318 827666 851392 983953 893802 964451 781952 959353 > 25¹⁰⁷ [i]