MinT - Best Known (32, 32+28, s)-Nets in Base 4

Best Known (32, 32+28, s)-Nets in Base 4

(32, 32+28, 66)-Net over F₄ — Constructive and digital

Digital (32, 60, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 30, 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, 32+28, 68)-Net over F₄ — Digital

Digital (32, 60, 68)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(32, 32+28, 755)-Net in Base 4 — Upper bound on s

There is no (32, 60, 756)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 340439 205641 527060 923869 121150 149220 > 4⁶⁰ [i]