MinT - Best Known (26, 26+59, s)-Nets in Base 25

Best Known (26, 26+59, s)-Nets in Base 25

(26, 26+59, 200)-Net over F₂₅ — Constructive and digital

Digital (26, 85, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 85, 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]

(26, 26+59, 5431)-Net in Base 25 — Upper bound on s

There is no (26, 85, 5432)-net in base 25, because

1 times m-reduction [i] would yield (26, 84, 5432)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2682 936838 385515 342924 641514 709497 134890 356995 076576 295710 715130 694024 930742 302056 518163 830786 800533 197636 033169 082945 > 25⁸⁴ [i]