MinT - Best Known (150, 150+44, s)-Nets in Base 3

Best Known (150, 150+44, s)-Nets in Base 3

(150, 150+44, 600)-Net over F₃ — Constructive and digital

Digital (150, 194, 600)-net over F₃, using

3² times duplication [i] based on 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]

(150, 150+44, 1221)-Net over F₃ — Digital

Digital (150, 194, 1221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+44, 72951)-Net in Base 3 — Upper bound on s

There is no (150, 194, 72952)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 356776 869509 750855 378423 631519 195890 302304 768875 156692 085324 846304 237126 818303 135155 996881 > 3¹⁹⁴ [i]