MinT - Best Known (28, 42, s)-Nets in Base 4

Best Known (28, 42, s)-Nets in Base 4

(28, 42, 195)-Net over F₄ — Constructive and digital

Digital (28, 42, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 14, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(28, 42, 4609)-Net in Base 4 — Upper bound on s

There is no (28, 42, 4610)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 19 357003 911649 692926 862592 > 4⁴² [i]