MinT - Best Known (237−56, 237, s)-Nets in Base 3

Best Known (237−56, 237, s)-Nets in Base 3

(237−56, 237, 464)-Net over F₃ — Constructive and digital

Digital (181, 237, 464)-net over F₃, using

3¹ times duplication [i] based on digital (180, 236, 464)-net over F₃, using
- t-expansion [i] based on digital (179, 236, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 59, 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]

(237−56, 237, 1228)-Net over F₃ — Digital

Digital (181, 237, 1228)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−56, 237, 61698)-Net in Base 3 — Upper bound on s

There is no (181, 237, 61699)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119647 689148 728476 026924 281650 481171 424858 524562 194065 239593 966930 769480 011653 270317 287991 205765 648552 584641 927465 > 3²³⁷ [i]