MinT - Best Known (135, 135+57, s)-Nets in Base 4

Best Known (135, 135+57, s)-Nets in Base 4

(135, 135+57, 531)-Net over F₄ — Constructive and digital

Digital (135, 192, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(135, 135+57, 838)-Net over F₄ — Digital

Digital (135, 192, 838)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+57, 48148)-Net in Base 4 — Upper bound on s

There is no (135, 192, 48149)-net in base 4, because

1 times m-reduction [i] would yield (135, 191, 48149)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 850588 143683 231332 684240 447273 518113 272048 283694 506432 325328 609304 745726 684579 540735 310324 873036 409963 734223 928448 > 4¹⁹¹ [i]