MinT - Best Known (172−40, 172, s)-Nets in Base 3

Best Known (172−40, 172, s)-Nets in Base 3

(172−40, 172, 464)-Net over F₃ — Constructive and digital

Digital (132, 172, 464)-net over F₃, using

t-expansion [i] based on digital (131, 172, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 43, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(172−40, 172, 998)-Net over F₃ — Digital

Digital (132, 172, 998)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−40, 172, 52645)-Net in Base 3 — Upper bound on s

There is no (132, 172, 52646)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11614 460245 771080 465432 762825 881443 471614 719111 588075 032075 884329 693744 035103 347881 > 3¹⁷² [i]