MinT - Best Known (156−39, 156, s)-Nets in Base 4

Best Known (156−39, 156, s)-Nets in Base 4

(156−39, 156, 1028)-Net over F₄ — Constructive and digital

Digital (117, 156, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 39, 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]

(156−39, 156, 1502)-Net over F₄ — Digital

Digital (117, 156, 1502)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−39, 156, 215578)-Net in Base 4 — Upper bound on s

There is no (117, 156, 215579)-net in base 4, because

1 times m-reduction [i] would yield (117, 155, 215579)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2086 021088 444443 833126 292786 656617 389380 118838 636992 803924 374147 458234 213325 318720 360624 289916 > 4¹⁵⁵ [i]