MinT - Best Known (128, 180, s)-Nets in Base 3

Best Known (128, 180, s)-Nets in Base 3

(128, 180, 252)-Net over F₃ — Constructive and digital

Digital (128, 180, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 60, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(128, 180, 458)-Net over F₃ — Digital

Digital (128, 180, 458)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 180, 10577)-Net in Base 3 — Upper bound on s

There is no (128, 180, 10578)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 350845 671073 351073 180558 587686 009861 319939 615240 767101 997888 867156 575925 920869 124453 > 3¹⁸⁰ [i]