MinT - Best Known (56−29, 56, s)-Nets in Base 5

Best Known (56−29, 56, s)-Nets in Base 5

(56−29, 56, 51)-Net over F₅ — Constructive and digital

Digital (27, 56, 51)-net over F₅, using

t-expansion [i] based on digital (22, 56, 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]

(56−29, 56, 60)-Net over F₅ — Digital

Digital (27, 56, 60)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−29, 56, 832)-Net in Base 5 — Upper bound on s

There is no (27, 56, 833)-net in base 5, because

1 times m-reduction [i] would yield (27, 55, 833)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 281 647851 647972 540421 171454 279095 976425 > 5⁵⁵ [i]