MinT - Best Known (98−75, 98, s)-Nets in Base 25

Best Known (98−75, 98, s)-Nets in Base 25

(98−75, 98, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 98, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 98, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(98−75, 98, 176)-Net over F₂₅ — Digital

Digital (23, 98, 176)-net over F₂₅, using

net from sequence [i] based on digital (23, 175)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 23 and N(F) ≥ 176, using
  - an algebraic function field by Teo [i]

(98−75, 98, 2802)-Net in Base 25 — Upper bound on s

There is no (23, 98, 2803)-net in base 25, because

1 times m-reduction [i] would yield (23, 97, 2803)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4004 971581 259448 613208 278791 651061 166373 421405 736172 359957 778988 730706 391899 368204 005417 967374 765785 284617 418195 345854 681435 436705 494505 > 25⁹⁷ [i]