MinT - Best Known (180−44, 180, s)-Nets in Base 3

Best Known (180−44, 180, s)-Nets in Base 3

(180−44, 180, 400)-Net over F₃ — Constructive and digital

Digital (136, 180, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 45, 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]

(180−44, 180, 855)-Net over F₃ — Digital

Digital (136, 180, 855)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−44, 180, 36248)-Net in Base 3 — Upper bound on s

There is no (136, 180, 36249)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 220157 755140 557724 224706 908817 916476 440402 832077 271103 082525 026248 134473 419585 448457 > 3¹⁸⁰ [i]