MinT - Best Known (180, 180+58, s)-Nets in Base 3

Best Known (180, 180+58, s)-Nets in Base 3

(180, 180+58, 400)-Net over F₃ — Constructive and digital

Digital (180, 238, 400)-net over F₃, using

3² times duplication [i] based on digital (178, 236, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 59, 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, 180+58, 1086)-Net over F₃ — Digital

Digital (180, 238, 1086)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+58, 48030)-Net in Base 3 — Upper bound on s

There is no (180, 238, 48031)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 358861 940319 698748 768607 142395 086780 390205 946713 354640 633983 352517 096957 717550 111222 870878 247450 454160 681354 019335 > 3²³⁸ [i]