MinT - Best Known (42−18, 42, s)-Nets in Base 4

Best Known (42−18, 42, s)-Nets in Base 4

(42−18, 42, 76)-Net over F₄ — Constructive and digital

Digital (24, 42, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 21, 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]

(42−18, 42, 884)-Net in Base 4 — Upper bound on s

There is no (24, 42, 885)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 19 387299 181254 752050 166512 > 4⁴² [i]