MinT - Best Known (28−14, 28, s)-Nets in Base 4

Best Known (28−14, 28, s)-Nets in Base 4

(28−14, 28, 34)-Net over F₄ — Constructive and digital

Digital (14, 28, 34)-net over F₄, using

trace code for nets [i] based on digital (0, 14, 17)-net over F₁₆, using
- net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
    - the rational function field F₁₆(x) [i]
  - Niederreiter sequence [i]

(28−14, 28, 35)-Net over F₄ — Digital

Digital (14, 28, 35)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(28−14, 28, 283)-Net in Base 4 — Upper bound on s

There is no (14, 28, 284)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 73586 661461 518210 > 4²⁸ [i]