MinT - Best Known (169, 220, s)-Nets in Base 3

Best Known (169, 220, s)-Nets in Base 3

(169, 220, 600)-Net over F₃ — Constructive and digital

Digital (169, 220, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 55, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(169, 220, 1249)-Net over F₃ — Digital

Digital (169, 220, 1249)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 220, 76920)-Net in Base 3 — Upper bound on s

There is no (169, 220, 76921)-net in base 3, because

1 times m-reduction [i] would yield (169, 219, 76921)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 308 805057 700199 500664 442466 016640 529818 238322 638373 882605 280842 520774 842788 522353 559915 669905 741016 240915 > 3²¹⁹ [i]