MinT - Best Known (123, 172, s)-Nets in Base 4

Best Known (123, 172, s)-Nets in Base 4

(123, 172, 531)-Net over F₄ — Constructive and digital

Digital (123, 172, 531)-net over F₄, using

2 times m-reduction [i] based on digital (123, 174, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 58, 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]

(123, 172, 915)-Net over F₄ — Digital

Digital (123, 172, 915)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 172, 63648)-Net in Base 4 — Upper bound on s

There is no (123, 172, 63649)-net in base 4, because

1 times m-reduction [i] would yield (123, 171, 63649)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 961792 894036 922742 821815 179890 742476 323947 905608 105853 723641 454699 398972 599037 947581 619562 451938 506284 > 4¹⁷¹ [i]