MinT - Best Known (29, 29+59, s)-Nets in Base 25

Best Known (29, 29+59, s)-Nets in Base 25

(29, 29+59, 200)-Net over F₂₅ — Constructive and digital

Digital (29, 88, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 88, 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]

(29, 29+59, 7583)-Net in Base 25 — Upper bound on s

There is no (29, 88, 7584)-net in base 25, because

1 times m-reduction [i] would yield (29, 87, 7584)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 41 865655 400158 981425 225473 114693 339711 336430 812617 607071 589692 293969 652616 475483 922446 216287 903513 971253 062229 951013 176065 > 25⁸⁷ [i]