MinT - Best Known (164−49, 164, s)-Nets in Base 3

Best Known (164−49, 164, s)-Nets in Base 3

(164−49, 164, 204)-Net over F₃ — Constructive and digital

Digital (115, 164, 204)-net over F₃, using

1 times m-reduction [i] based on digital (115, 165, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 55, 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]

(164−49, 164, 379)-Net over F₃ — Digital

Digital (115, 164, 379)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−49, 164, 8503)-Net in Base 3 — Upper bound on s

There is no (115, 164, 8504)-net in base 3, because

1 times m-reduction [i] would yield (115, 163, 8504)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 591156 740699 496852 998791 594385 316482 241103 238986 553626 024416 596675 554072 657153 > 3¹⁶³ [i]