MinT - Best Known (104−77, 104, s)-Nets in Base 25

Best Known (104−77, 104, s)-Nets in Base 25

(104−77, 104, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 104, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 104, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(104−77, 104, 3832)-Net in Base 25 — Upper bound on s

There is no (27, 104, 3833)-net in base 25, because

1 times m-reduction [i] would yield (27, 103, 3833)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 977519 315692 125516 660051 621355 655315 268085 494703 659239 779955 020728 984476 595492 526833 406009 528279 545523 531682 252760 357084 041690 270520 863575 990225 > 25¹⁰³ [i]