MinT - Best Known (83−45, 83, s)-Nets in Base 3

Best Known (83−45, 83, s)-Nets in Base 3

(83−45, 83, 38)-Net over F₃ — Constructive and digital

Digital (38, 83, 38)-net over F₃, using

t-expansion [i] based on digital (32, 83, 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]

(83−45, 83, 52)-Net over F₃ — Digital

Digital (38, 83, 52)-net over F₃, using

t-expansion [i] based on digital (37, 83, 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]

(83−45, 83, 250)-Net in Base 3 — Upper bound on s

There is no (38, 83, 251)-net in base 3, because

1 times m-reduction [i] would yield (38, 82, 251)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1336 606336 104359 641458 836077 287121 227309 > 3⁸² [i]