MinT - Best Known (42−37, 42, s)-Nets in Base 25

Best Known (42−37, 42, s)-Nets in Base 25

(42−37, 42, 66)-Net over F₂₅ — Constructive and digital

Digital (5, 42, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 42, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(42−37, 42, 471)-Net in Base 25 — Upper bound on s

There is no (5, 42, 472)-net in base 25, because

1 times m-reduction [i] would yield (5, 41, 472)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2086 694391 597573 576369 884647 326159 284174 723248 491503 992705 > 25⁴¹ [i]