MinT - Best Known (100, 135, s)-Nets in Base 3

Best Known (100, 135, s)-Nets in Base 3

(100, 135, 282)-Net over F₃ — Constructive and digital

Digital (100, 135, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 45, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(100, 135, 542)-Net over F₃ — Digital

Digital (100, 135, 542)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 135, 20673)-Net in Base 3 — Upper bound on s

There is no (100, 135, 20674)-net in base 3, because

1 times m-reduction [i] would yield (100, 134, 20674)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8600 945678 182146 292113 002076 517479 799740 311775 691939 505671 355877 > 3¹³⁴ [i]