MinT - Best Known (237−57, 237, s)-Nets in Base 3

Best Known (237−57, 237, s)-Nets in Base 3

(237−57, 237, 464)-Net over F₃ — Constructive and digital

Digital (180, 237, 464)-net over F₃, using

3¹ times duplication [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]

(237−57, 237, 1141)-Net over F₃ — Digital

Digital (180, 237, 1141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−57, 237, 59323)-Net in Base 3 — Upper bound on s

There is no (180, 237, 59324)-net in base 3, because

1 times m-reduction [i] would yield (180, 236, 59324)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39882 791595 988170 213381 980274 156179 392687 143830 572383 597975 976553 150393 493965 142336 801461 450645 982597 522735 785665 > 3²³⁶ [i]