MinT - Best Known (99−71, 99, s)-Nets in Base 25

Best Known (99−71, 99, s)-Nets in Base 25

(99−71, 99, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 99, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 99, 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]

(99−71, 99, 4738)-Net in Base 25 — Upper bound on s

There is no (28, 99, 4739)-net in base 25, because

1 times m-reduction [i] would yield (28, 98, 4739)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 100284 549359 996653 959311 186856 046496 977432 427687 433698 498752 568273 104303 879355 141991 430853 162609 180936 529101 441877 788193 968170 928517 089881 > 25⁹⁸ [i]