MinT - Best Known (98−59, 98, s)-Nets in Base 25

Best Known (98−59, 98, s)-Nets in Base 25

(98−59, 98, 208)-Net over F₂₅ — Constructive and digital

Digital (39, 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]

(98−59, 98, 23040)-Net in Base 25 — Upper bound on s

There is no (39, 98, 23041)-net in base 25, because

1 times m-reduction [i] would yield (39, 97, 23041)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3985 058369 125978 576048 559426 897210 745251 894915 607282 327092 302870 463100 782141 065457 986140 355866 665343 739877 240364 976421 205109 717221 603385 > 25⁹⁷ [i]