MinT - Best Known (175−49, 175, s)-Nets in Base 4

Best Known (175−49, 175, s)-Nets in Base 4

(175−49, 175, 531)-Net over F₄ — Constructive and digital

Digital (126, 175, 531)-net over F₄, using

t-expansion [i] based on digital (125, 175, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (125, 177, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 59, 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]

(175−49, 175, 1003)-Net over F₄ — Digital

Digital (126, 175, 1003)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−49, 175, 75694)-Net in Base 4 — Upper bound on s

There is no (126, 175, 75695)-net in base 4, because

1 times m-reduction [i] would yield (126, 174, 75695)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 457960 537634 331292 450994 194852 721862 648734 633090 369153 981436 510704 669750 839259 382708 632880 907636 648294 > 4¹⁷⁴ [i]