MinT - Best Known (81−43, 81, s)-Nets in Base 3

Best Known (81−43, 81, s)-Nets in Base 3

(81−43, 81, 38)-Net over F₃ — Constructive and digital

Digital (38, 81, 38)-net over F₃, using

t-expansion [i] based on digital (32, 81, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(81−43, 81, 52)-Net over F₃ — Digital

Digital (38, 81, 52)-net over F₃, using

t-expansion [i] based on digital (37, 81, 52)-net over F₃, using
- net from sequence [i] based on digital (37, 51)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 37 and N(F) ≥ 52, using
    - a curve from the manYPoints database [i]

(81−43, 81, 265)-Net in Base 3 — Upper bound on s

There is no (38, 81, 266)-net in base 3, because

1 times m-reduction [i] would yield (38, 80, 266)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 156 327227 198719 321983 881934 781263 157709 > 3⁸⁰ [i]