MinT - Best Known (138, 138+54, s)-Nets in Base 3

Best Known (138, 138+54, s)-Nets in Base 3

(138, 138+54, 282)-Net over F₃ — Constructive and digital

Digital (138, 192, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 64, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(138, 138+54, 531)-Net over F₃ — Digital

Digital (138, 192, 531)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+54, 13470)-Net in Base 3 — Upper bound on s

There is no (138, 192, 13471)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 518027 283287 419892 284050 751144 082320 718401 536534 315884 964266 886981 099048 327855 554039 369291 > 3¹⁹² [i]