MinT - Best Known (98−61, 98, s)-Nets in Base 25

Best Known (98−61, 98, s)-Nets in Base 25

(98−61, 98, 208)-Net over F₂₅ — Constructive and digital

Digital (37, 98, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 98, 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]

(98−61, 98, 16602)-Net in Base 25 — Upper bound on s

There is no (37, 98, 16603)-net in base 25, because

1 times m-reduction [i] would yield (37, 97, 16603)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3986 806516 770365 297546 665964 072198 520542 534064 292000 467599 015309 744761 214285 112940 935068 960749 826167 605565 336194 102231 047939 513178 083185 > 25⁹⁷ [i]