MinT - Best Known (85−47, 85, s)-Nets in Base 3

Best Known (85−47, 85, s)-Nets in Base 3

(85−47, 85, 38)-Net over F₃ — Constructive and digital

Digital (38, 85, 38)-net over F₃, using

t-expansion [i] based on digital (32, 85, 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]

(85−47, 85, 52)-Net over F₃ — Digital

Digital (38, 85, 52)-net over F₃, using

t-expansion [i] based on digital (37, 85, 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]

(85−47, 85, 238)-Net in Base 3 — Upper bound on s

There is no (38, 85, 239)-net in base 3, because

1 times m-reduction [i] would yield (38, 84, 239)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 12115 983211 214581 027036 255959 067642 249875 > 3⁸⁴ [i]