MinT - Best Known (63, 63+57, s)-Nets in Base 4

Best Known (63, 63+57, s)-Nets in Base 4

(63, 63+57, 76)-Net over F₄ — Constructive and digital

Digital (63, 120, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 60, 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]

(63, 63+57, 109)-Net over F₄ — Digital

Digital (63, 120, 109)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+57, 1340)-Net in Base 4 — Upper bound on s

There is no (63, 120, 1341)-net in base 4, because

1 times m-reduction [i] would yield (63, 119, 1341)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 443884 896433 296848 563390 460257 632634 652411 815158 259543 240011 120094 838707 > 4¹¹⁹ [i]