MinT - Best Known (192−44, 192, s)-Nets in Base 3

Best Known (192−44, 192, s)-Nets in Base 3

(192−44, 192, 600)-Net over F₃ — Constructive and digital

Digital (148, 192, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 48, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(192−44, 192, 1161)-Net over F₃ — Digital

Digital (148, 192, 1161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−44, 192, 66015)-Net in Base 3 — Upper bound on s

There is no (148, 192, 66016)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 484297 709628 799076 771887 359391 377743 419621 947820 704982 965461 409046 818500 663622 169008 483137 > 3¹⁹² [i]