MinT - Best Known (78−49, 78, s)-Nets in Base 25

Best Known (78−49, 78, s)-Nets in Base 25

(78−49, 78, 200)-Net over F₂₅ — Constructive and digital

Digital (29, 78, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 78, 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]

(78−49, 78, 12467)-Net in Base 25 — Upper bound on s

There is no (29, 78, 12468)-net in base 25, because

1 times m-reduction [i] would yield (29, 77, 12468)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 438459 371929 395732 971755 526333 289680 383076 206683 688320 236192 787366 737742 873393 093115 663062 547075 070171 361025 > 25⁷⁷ [i]