MinT - Best Known (165, 165+75, s)-Nets in Base 3

Best Known (165, 165+75, s)-Nets in Base 3

(165, 165+75, 204)-Net over F₃ — Constructive and digital

Digital (165, 240, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 80, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(165, 165+75, 457)-Net over F₃ — Digital

Digital (165, 240, 457)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+75, 8811)-Net in Base 3 — Upper bound on s

There is no (165, 240, 8812)-net in base 3, because

1 times m-reduction [i] would yield (165, 239, 8812)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 080031 110710 884721 706471 758400 596046 118209 026454 279096 176931 638029 637738 417242 010346 717082 514588 079361 248400 102329 > 3²³⁹ [i]