MinT - Best Known (45−24, 45, s)-Nets in Base 3

Best Known (45−24, 45, s)-Nets in Base 3

(45−24, 45, 32)-Net over F₃ — Constructive and digital

Digital (21, 45, 32)-net over F₃, using

net from sequence [i] based on digital (21, 31)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(45−24, 45, 151)-Net in Base 3 — Upper bound on s

There is no (21, 45, 152)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3046 242908 491319 973569 > 3⁴⁵ [i]