MinT - Best Known (45, 45+37, s)-Nets in Base 5

Best Known (45, 45+37, s)-Nets in Base 5

(45, 45+37, 132)-Net over F₅ — Constructive and digital

Digital (45, 82, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 41, 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]

(45, 45+37, 2625)-Net in Base 5 — Upper bound on s

There is no (45, 82, 2626)-net in base 5, because

1 times m-reduction [i] would yield (45, 81, 2626)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 413 598765 198159 502692 479876 036489 348318 089118 818438 626625 > 5⁸¹ [i]