MinT - Best Known (133, 133+44, s)-Nets in Base 3

Best Known (133, 133+44, s)-Nets in Base 3

(133, 133+44, 328)-Net over F₃ — Constructive and digital

Digital (133, 177, 328)-net over F₃, using

3¹ times duplication [i] based on digital (132, 176, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 44, 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]

(133, 133+44, 788)-Net over F₃ — Digital

Digital (133, 177, 788)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+44, 31201)-Net in Base 3 — Upper bound on s

There is no (133, 177, 31202)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 821540 312399 700192 195725 855931 486616 592711 597045 322406 561179 133263 536242 684818 378781 > 3¹⁷⁷ [i]