MinT - Best Known (56, 56+55, s)-Nets in Base 5

Best Known (56, 56+55, s)-Nets in Base 5

(56, 56+55, 82)-Net over F₅ — Constructive and digital

Digital (56, 111, 82)-net over F₅, using

t-expansion [i] based on digital (48, 111, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(56, 56+55, 117)-Net over F₅ — Digital

Digital (56, 111, 117)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+55, 1903)-Net in Base 5 — Upper bound on s

There is no (56, 111, 1904)-net in base 5, because

1 times m-reduction [i] would yield (56, 110, 1904)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77662 009019 845495 249015 547732 356585 501025 391642 483818 647475 477580 447842 565057 > 5¹¹⁰ [i]