MinT - Best Known (133, 133+43, s)-Nets in Base 3

Best Known (133, 133+43, s)-Nets in Base 3

(133, 133+43, 400)-Net over F₃ — Constructive and digital

Digital (133, 176, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 44, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(133, 133+43, 842)-Net over F₃ — Digital

Digital (133, 176, 842)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+43, 41044)-Net in Base 3 — Upper bound on s

There is no (133, 176, 41045)-net in base 3, because

1 times m-reduction [i] would yield (133, 175, 41045)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313548 308424 534393 147095 614385 688742 004152 843481 674405 707857 050086 013020 731490 543483 > 3¹⁷⁵ [i]