MinT - Best Known (235−69, 235, s)-Nets in Base 4

Best Known (235−69, 235, s)-Nets in Base 4

(235−69, 235, 531)-Net over F₄ — Constructive and digital

Digital (166, 235, 531)-net over F₄, using

t-expansion [i] based on digital (165, 235, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (165, 237, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 79, 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]

(235−69, 235, 1041)-Net over F₄ — Digital

Digital (166, 235, 1041)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−69, 235, 62769)-Net in Base 4 — Upper bound on s

There is no (166, 235, 62770)-net in base 4, because

1 times m-reduction [i] would yield (166, 234, 62770)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 762 211291 402481 688350 091482 602233 374051 485394 381653 921816 049070 492825 285794 553664 251572 475174 886652 586264 461861 779694 226774 753709 149664 646032 > 4²³⁴ [i]