MinT - Best Known (63, 63+54, s)-Nets in Base 4

Best Known (63, 63+54, s)-Nets in Base 4

(63, 63+54, 90)-Net over F₄ — Constructive and digital

Digital (63, 117, 90)-net over F₄, using

1 times m-reduction [i] based on digital (63, 118, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 59, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(63, 63+54, 118)-Net over F₄ — Digital

Digital (63, 117, 118)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+54, 1457)-Net in Base 4 — Upper bound on s

There is no (63, 117, 1458)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27629 148607 688288 016168 838595 345570 213960 832367 054846 322407 868285 908144 > 4¹¹⁷ [i]