MinT - Best Known (192−59, 192, s)-Nets in Base 3

Best Known (192−59, 192, s)-Nets in Base 3

(192−59, 192, 204)-Net over F₃ — Constructive and digital

Digital (133, 192, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 64, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(192−59, 192, 396)-Net over F₃ — Digital

Digital (133, 192, 396)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−59, 192, 8072)-Net in Base 3 — Upper bound on s

There is no (133, 192, 8073)-net in base 3, because

1 times m-reduction [i] would yield (133, 191, 8073)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 541403 843126 263578 386989 519729 826029 384886 615660 892818 337356 819581 468086 123540 876791 781283 > 3¹⁹¹ [i]