MinT - Best Known (62, 62+56, s)-Nets in Base 4

Best Known (62, 62+56, s)-Nets in Base 4

(62, 62+56, 76)-Net over F₄ — Constructive and digital

Digital (62, 118, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 59, 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]

(62, 62+56, 108)-Net over F₄ — Digital

Digital (62, 118, 108)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+56, 1274)-Net in Base 4 — Upper bound on s

There is no (62, 118, 1275)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110649 336883 310084 028360 393632 703583 396651 479048 280953 607081 429473 980344 > 4¹¹⁸ [i]