MinT - Best Known (68−34, 68, s)-Nets in Base 3

Best Known (68−34, 68, s)-Nets in Base 3

(68−34, 68, 38)-Net over F₃ — Constructive and digital

Digital (34, 68, 38)-net over F₃, using

t-expansion [i] based on digital (32, 68, 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]

(68−34, 68, 46)-Net over F₃ — Digital

Digital (34, 68, 46)-net over F₃, using

t-expansion [i] based on digital (33, 68, 46)-net over F₃, using
- net from sequence [i] based on digital (33, 45)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 33 and N(F) ≥ 46, using
    - a curve from the manYPoints database [i]

(68−34, 68, 274)-Net in Base 3 — Upper bound on s

There is no (34, 68, 275)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 285 537012 439890 658892 565052 025991 > 3⁶⁸ [i]