MinT - Best Known (62−28, 62, s)-Nets in Base 4

Best Known (62−28, 62, s)-Nets in Base 4

(62−28, 62, 76)-Net over F₄ — Constructive and digital

Digital (34, 62, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 31, 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]

(62−28, 62, 78)-Net over F₄ — Digital

Digital (34, 62, 78)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−28, 62, 923)-Net in Base 4 — Upper bound on s

There is no (34, 62, 924)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 21 448639 650041 799314 841121 352110 503004 > 4⁶² [i]