MinT - Best Known (26, 26+51, s)-Nets in Base 25

Best Known (26, 26+51, s)-Nets in Base 25

(26, 26+51, 200)-Net over F₂₅ — Constructive and digital

Digital (26, 77, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 77, 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+51, 7523)-Net in Base 25 — Upper bound on s

There is no (26, 77, 7524)-net in base 25, because

1 times m-reduction [i] would yield (26, 76, 7524)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 17565 107535 674542 254607 777616 263588 376341 028293 411045 223267 782432 718573 296448 084890 990640 429512 744349 257825 > 25⁷⁶ [i]