MinT - Best Known (145−81, 145, s)-Nets in Base 3

Best Known (145−81, 145, s)-Nets in Base 3

(145−81, 145, 48)-Net over F₃ — Constructive and digital

Digital (64, 145, 48)-net over F₃, using

t-expansion [i] based on digital (45, 145, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(145−81, 145, 64)-Net over F₃ — Digital

Digital (64, 145, 64)-net over F₃, using

t-expansion [i] based on digital (49, 145, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(145−81, 145, 373)-Net in Base 3 — Upper bound on s

There is no (64, 145, 374)-net in base 3, because

1 times m-reduction [i] would yield (64, 144, 374)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 531 337908 486341 879291 271161 291057 264286 402024 819874 312131 339347 165201 > 3¹⁴⁴ [i]