MinT - Best Known (87−52, 87, s)-Nets in Base 3

Best Known (87−52, 87, s)-Nets in Base 3

(87−52, 87, 38)-Net over F₃ — Constructive and digital

Digital (35, 87, 38)-net over F₃, using

t-expansion [i] based on digital (32, 87, 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]

(87−52, 87, 47)-Net over F₃ — Digital

Digital (35, 87, 47)-net over F₃, using

net from sequence [i] based on digital (35, 46)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 35 and N(F) ≥ 47, using
  - a curve from the manYPoints database [i]

(87−52, 87, 184)-Net in Base 3 — Upper bound on s

There is no (35, 87, 185)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 363183 026916 077939 530270 538045 674555 238937 > 3⁸⁷ [i]