MinT - Best Known (50, 50+44, s)-Nets in Base 4

Best Known (50, 50+44, s)-Nets in Base 4

(50, 50+44, 76)-Net over F₄ — Constructive and digital

Digital (50, 94, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 47, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(50, 50+44, 94)-Net over F₄ — Digital

Digital (50, 94, 94)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+44, 1109)-Net in Base 4 — Upper bound on s

There is no (50, 94, 1110)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 392 983588 800137 115398 879173 283397 838508 161637 152717 943224 > 4⁹⁴ [i]