MinT - Best Known (56−19, 56, s)-Nets in Base 5

Best Known (56−19, 56, s)-Nets in Base 5

(56−19, 56, 208)-Net over F₅ — Constructive and digital

Digital (37, 56, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 28, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(56−19, 56, 291)-Net over F₅ — Digital

Digital (37, 56, 291)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−19, 56, 19365)-Net in Base 5 — Upper bound on s

There is no (37, 56, 19366)-net in base 5, because

1 times m-reduction [i] would yield (37, 55, 19366)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 277 585848 831215 420409 935861 385237 627545 > 5⁵⁵ [i]