MinT - Best Known (42, 42+22, s)-Nets in Base 3

Best Known (42, 42+22, s)-Nets in Base 3

(42, 42+22, 80)-Net over F₃ — Constructive and digital

Digital (42, 64, 80)-net over F₃, using

4 times m-reduction [i] based on digital (42, 68, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 34, 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]

(42, 42+22, 118)-Net over F₃ — Digital

Digital (42, 64, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+22, 1454)-Net in Base 3 — Upper bound on s

There is no (42, 64, 1455)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 434913 288736 623761 161824 882859 > 3⁶⁴ [i]