MinT - Best Known (62−27, 62, s)-Nets in Base 3

Best Known (62−27, 62, s)-Nets in Base 3

(62−27, 62, 60)-Net over F₃ — Constructive and digital

Digital (35, 62, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 31, 30)-net over F₉, using
- net from sequence [i] based on digital (4, 29)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [i]

(62−27, 62, 478)-Net in Base 3 — Upper bound on s

There is no (35, 62, 479)-net in base 3, because

1 times m-reduction [i] would yield (35, 61, 479)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 128057 186234 600071 214586 385575 > 3⁶¹ [i]