MinT - Best Known (42, 42+14, s)-Nets in Base 4

Best Known (42, 42+14, s)-Nets in Base 4

(42, 42+14, 1028)-Net over F₄ — Constructive and digital

Digital (42, 56, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 14, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(42, 42+14, 73832)-Net in Base 4 — Upper bound on s

There is no (42, 56, 73833)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5192 678535 059650 767221 048233 870216 > 4⁵⁶ [i]