MinT - Best Known (133−36, 133, s)-Nets in Base 3

Best Known (133−36, 133, s)-Nets in Base 3

(133−36, 133, 252)-Net over F₃ — Constructive and digital

Digital (97, 133, 252)-net over F₃, using

3¹ times duplication [i] based on digital (96, 132, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 44, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(133−36, 133, 454)-Net over F₃ — Digital

Digital (97, 133, 454)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−36, 133, 12644)-Net in Base 3 — Upper bound on s

There is no (97, 133, 12645)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2867 760682 779851 006788 038201 440138 882408 539397 096822 583946 289745 > 3¹³³ [i]