MinT - Best Known (150, 150+45, s)-Nets in Base 3

Best Known (150, 150+45, s)-Nets in Base 3

(150, 150+45, 464)-Net over F₃ — Constructive and digital

Digital (150, 195, 464)-net over F₃, using

t-expansion [i] based on digital (149, 195, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (149, 196, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 49, 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]

(150, 150+45, 1145)-Net over F₃ — Digital

Digital (150, 195, 1145)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+45, 72951)-Net in Base 3 — Upper bound on s

There is no (150, 195, 72952)-net in base 3, because

1 times m-reduction [i] would yield (150, 194, 72952)-net in base 3, but
- 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]