MinT - Best Known (46−18, 46, s)-Nets in Base 4

Best Known (46−18, 46, s)-Nets in Base 4

(46−18, 46, 98)-Net over F₄ — Constructive and digital

Digital (28, 46, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 23, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(46−18, 46, 103)-Net over F₄ — Digital

Digital (28, 46, 103)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(46−18, 46, 1644)-Net in Base 4 — Upper bound on s

There is no (28, 46, 1645)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4970 396222 427315 875696 277328 > 4⁴⁶ [i]