MinT - Best Known (52, 52+32, s)-Nets in Base 3

Best Known (52, 52+32, s)-Nets in Base 3

(52, 52+32, 80)-Net over F₃ — Constructive and digital

Digital (52, 84, 80)-net over F₃, using

4 times m-reduction [i] based on digital (52, 88, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 44, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(52, 52+32, 108)-Net over F₃ — Digital

Digital (52, 84, 108)-net over F₃, using

trace code for nets [i] based on digital (10, 42, 54)-net over F₉, using
- net from sequence [i] based on digital (10, 53)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
    - a curve from the manYPoints database [i]

(52, 52+32, 1072)-Net in Base 3 — Upper bound on s

There is no (52, 84, 1073)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 12148 692160 387483 956246 868344 406758 529857 > 3⁸⁴ [i]