MinT - Best Known (68−32, 68, s)-Nets in Base 4

Best Known (68−32, 68, s)-Nets in Base 4

(68−32, 68, 66)-Net over F₄ — Constructive and digital

Digital (36, 68, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 34, 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]

(68−32, 68, 72)-Net over F₄ — Digital

Digital (36, 68, 72)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(68−32, 68, 807)-Net in Base 4 — Upper bound on s

There is no (36, 68, 808)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 87246 028207 800955 563192 068036 896256 918350 > 4⁶⁸ [i]