MinT - Best Known (240−57, 240, s)-Nets in Base 3

Best Known (240−57, 240, s)-Nets in Base 3

(240−57, 240, 464)-Net over F₃ — Constructive and digital

Digital (183, 240, 464)-net over F₃, using

t-expansion [i] based on digital (182, 240, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 60, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(240−57, 240, 1215)-Net over F₃ — Digital

Digital (183, 240, 1215)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−57, 240, 66737)-Net in Base 3 — Upper bound on s

There is no (183, 240, 66738)-net in base 3, because

1 times m-reduction [i] would yield (183, 239, 66738)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 076854 816179 821263 644967 623251 413305 978157 575150 042385 140025 902170 515880 680990 182286 976124 974198 902095 811466 992921 > 3²³⁹ [i]