MinT - Best Known (105−77, 105, s)-Nets in Base 25

Best Known (105−77, 105, s)-Nets in Base 25

(105−77, 105, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 105, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 105, 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]

(105−77, 105, 4173)-Net in Base 25 — Upper bound on s

There is no (28, 105, 4174)-net in base 25, because

1 times m-reduction [i] would yield (28, 104, 4174)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 24 526177 659609 425116 439466 137980 769073 466914 353823 595939 703364 722631 088033 883372 553790 657440 688623 333889 643831 365137 574603 268604 428074 868816 441761 > 25¹⁰⁴ [i]