MinT - Best Known (45−23, 45, s)-Nets in Base 5

Best Known (45−23, 45, s)-Nets in Base 5

(45−23, 45, 51)-Net over F₅ — Constructive and digital

Digital (22, 45, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(45−23, 45, 54)-Net over F₅ — Digital

Digital (22, 45, 54)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(45−23, 45, 759)-Net in Base 5 — Upper bound on s

There is no (22, 45, 760)-net in base 5, because

1 times m-reduction [i] would yield (22, 44, 760)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 737771 373342 742038 895432 089825 > 5⁴⁴ [i]