MinT - Best Known (68, 68+62, s)-Nets in Base 4

Best Known (68, 68+62, s)-Nets in Base 4

(68, 68+62, 76)-Net over F₄ — Constructive and digital

Digital (68, 130, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 65, 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]

(68, 68+62, 115)-Net over F₄ — Digital

Digital (68, 130, 115)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+62, 1360)-Net in Base 4 — Upper bound on s

There is no (68, 130, 1361)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 870350 796570 188728 321297 021696 505775 892886 276262 311083 443883 496755 100240 047680 > 4¹³⁰ [i]