MinT - Best Known (16, 16+12, s)-Nets in Base 4

Best Known (16, 16+12, s)-Nets in Base 4

(16, 16+12, 66)-Net over F₄ — Constructive and digital

Digital (16, 28, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 14, 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]

(16, 16+12, 639)-Net in Base 4 — Upper bound on s

There is no (16, 28, 640)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 72557 403726 165985 > 4²⁸ [i]