MinT - Best Known (32−14, 32, s)-Nets in Base 4

Best Known (32−14, 32, s)-Nets in Base 4

(32−14, 32, 66)-Net over F₄ — Constructive and digital

Digital (18, 32, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 16, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(32−14, 32, 631)-Net in Base 4 — Upper bound on s

There is no (18, 32, 632)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 18 531055 492803 460195 > 4³² [i]