MinT - Best Known (213−53, 213, s)-Nets in Base 3

Best Known (213−53, 213, s)-Nets in Base 3

(213−53, 213, 328)-Net over F₃ — Constructive and digital

Digital (160, 213, 328)-net over F₃, using

3¹ times duplication [i] based on digital (159, 212, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 53, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(213−53, 213, 911)-Net over F₃ — Digital

Digital (160, 213, 911)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−53, 213, 40960)-Net in Base 3 — Upper bound on s

There is no (160, 213, 40961)-net in base 3, because

1 times m-reduction [i] would yield (160, 212, 40961)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141195 453179 093674 895059 164821 663860 425087 011273 016200 724737 578489 519666 713443 374289 619048 481781 104617 > 3²¹² [i]