MinT - Best Known (110−73, 110, s)-Nets in Base 25

Best Known (110−73, 110, s)-Nets in Base 25

(110−73, 110, 208)-Net over F₂₅ — Constructive and digital

Digital (37, 110, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 110, 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]

(110−73, 110, 10147)-Net in Base 25 — Upper bound on s

There is no (37, 110, 10148)-net in base 25, because

1 times m-reduction [i] would yield (37, 109, 10148)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 237 683431 255631 122709 436918 319644 983900 237653 218083 584980 263006 555216 327453 489519 560588 061336 877878 875072 212592 088917 910678 065555 207915 252479 453492 883585 > 25¹⁰⁹ [i]