MinT - Best Known (99−63, 99, s)-Nets in Base 25

Best Known (99−63, 99, s)-Nets in Base 25

(99−63, 99, 208)-Net over F₂₅ — Constructive and digital

Digital (36, 99, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 99, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(99−63, 99, 13570)-Net in Base 25 — Upper bound on s

There is no (36, 99, 13571)-net in base 25, because

1 times m-reduction [i] would yield (36, 98, 13571)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 99687 838299 081445 594352 629758 333600 158946 832175 099428 276450 832392 795185 731848 963508 982542 892930 576965 959398 899841 747823 413467 609829 902905 > 25⁹⁸ [i]