MinT - Best Known (138, 138+46, s)-Nets in Base 3

Best Known (138, 138+46, s)-Nets in Base 3

(138, 138+46, 328)-Net over F₃ — Constructive and digital

Digital (138, 184, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 46, 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]

(138, 138+46, 794)-Net over F₃ — Digital

Digital (138, 184, 794)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+46, 30908)-Net in Base 3 — Upper bound on s

There is no (138, 184, 30909)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6171 856671 268140 107225 775834 258556 842936 846964 589575 957412 498291 172687 463351 879299 833595 > 3¹⁸⁴ [i]