MinT - Best Known (95−79, 95, s)-Nets in Base 25

Best Known (95−79, 95, s)-Nets in Base 25

(95−79, 95, 126)-Net over F₂₅ — Constructive and digital

Digital (16, 95, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 95, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(95−79, 95, 150)-Net over F₂₅ — Digital

Digital (16, 95, 150)-net over F₂₅, using

net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
  - an algebraic function field by Teo [i]

(95−79, 95, 1481)-Net in Base 25 — Upper bound on s

There is no (16, 95, 1482)-net in base 25, because

1 times m-reduction [i] would yield (16, 94, 1482)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 260083 539044 874305 050816 126619 946730 862506 927620 135774 954805 872853 833270 637445 679010 331406 170318 906208 348322 310255 476016 357779 135825 > 25⁹⁴ [i]