MinT - Best Known (125, 125+55, s)-Nets in Base 4

Best Known (125, 125+55, s)-Nets in Base 4

(125, 125+55, 384)-Net over F₄ — Constructive and digital

Digital (125, 180, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 60, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(125, 125+55, 704)-Net over F₄ — Digital

Digital (125, 180, 704)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+55, 35682)-Net in Base 4 — Upper bound on s

There is no (125, 180, 35683)-net in base 4, because

1 times m-reduction [i] would yield (125, 179, 35683)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 587453 347956 811901 321884 392074 346448 149384 404701 713085 473432 700564 638400 957576 375869 324569 971491 456137 389840 > 4¹⁷⁹ [i]