MinT - Best Known (36, 36+42, s)-Nets in Base 3

Best Known (36, 36+42, s)-Nets in Base 3

(36, 36+42, 38)-Net over F₃ — Constructive and digital

Digital (36, 78, 38)-net over F₃, using

t-expansion [i] based on digital (32, 78, 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]

(36, 36+42, 48)-Net over F₃ — Digital

Digital (36, 78, 48)-net over F₃, using

net from sequence [i] based on digital (36, 47)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 36 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(36, 36+42, 236)-Net in Base 3 — Upper bound on s

There is no (36, 78, 237)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 456154 163707 458206 061123 453081 980075 > 3⁷⁸ [i]