MinT - Best Known (56−20, 56, s)-Nets in Base 3

Best Known (56−20, 56, s)-Nets in Base 3

(56−20, 56, 80)-Net over F₃ — Constructive and digital

Digital (36, 56, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 28, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(56−20, 56, 96)-Net over F₃ — Digital

Digital (36, 56, 96)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−20, 56, 1054)-Net in Base 3 — Upper bound on s

There is no (36, 56, 1055)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 527 046651 010386 818944 671789 > 3⁵⁶ [i]