MinT - Best Known (53, 53+47, s)-Nets in Base 3

Best Known (53, 53+47, s)-Nets in Base 3

(53, 53+47, 56)-Net over F₃ — Constructive and digital

Digital (53, 100, 56)-net over F₃, using

trace code for nets [i] based on digital (3, 50, 28)-net over F₉, using
- net from sequence [i] based on digital (3, 27)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]

(53, 53+47, 67)-Net over F₃ — Digital

Digital (53, 100, 67)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+47, 511)-Net in Base 3 — Upper bound on s

There is no (53, 100, 512)-net in base 3, because

1 times m-reduction [i] would yield (53, 99, 512)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 176501 587805 457049 206004 739241 898859 905703 057409 > 3⁹⁹ [i]