MinT - Best Known (95−81, 95, s)-Nets in Base 25

Best Known (95−81, 95, s)-Nets in Base 25

(95−81, 95, 126)-Net over F₂₅ — Constructive and digital

Digital (14, 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]

(95−81, 95, 130)-Net over F₂₅ — Digital

Digital (14, 95, 130)-net over F₂₅, using

net from sequence [i] based on digital (14, 129)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 14 and N(F) ≥ 130, using
  - an algebraic function field by Teo [i]

(95−81, 95, 1245)-Net in Base 25 — Upper bound on s

There is no (14, 95, 1246)-net in base 25, because

1 times m-reduction [i] would yield (14, 94, 1246)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 256490 303397 615106 704962 060309 493856 152506 832748 677790 258295 457889 123488 438071 908388 129860 136529 876473 343405 244481 620402 334189 923201 > 25⁹⁴ [i]