MinT - Best Known (148, 148+45, s)-Nets in Base 3

Best Known (148, 148+45, s)-Nets in Base 3

(148, 148+45, 464)-Net over F₃ — Constructive and digital

Digital (148, 193, 464)-net over F₃, using

3¹ times duplication [i] based on digital (147, 192, 464)-net over F₃, using
- t-expansion [i] based on digital (146, 192, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 48, 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]

(148, 148+45, 1090)-Net over F₃ — Digital

Digital (148, 193, 1090)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+45, 66015)-Net in Base 3 — Upper bound on s

There is no (148, 193, 66016)-net in base 3, because

1 times m-reduction [i] would yield (148, 192, 66016)-net in base 3, but
- 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]