MinT - Best Known (52−27, 52, s)-Nets in Base 5

Best Known (52−27, 52, s)-Nets in Base 5

(52−27, 52, 51)-Net over F₅ — Constructive and digital

Digital (25, 52, 51)-net over F₅, using

t-expansion [i] based on digital (22, 52, 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]

(52−27, 52, 56)-Net over F₅ — Digital

Digital (25, 52, 56)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(52−27, 52, 773)-Net in Base 5 — Upper bound on s

There is no (25, 52, 774)-net in base 5, because

1 times m-reduction [i] would yield (25, 51, 774)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 449694 537835 885509 750568 005802 127769 > 5⁵¹ [i]