MinT - Best Known (124, 124+48, s)-Nets in Base 4

Best Known (124, 124+48, s)-Nets in Base 4

(124, 124+48, 531)-Net over F₄ — Constructive and digital

Digital (124, 172, 531)-net over F₄, using

t-expansion [i] based on 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]

(124, 124+48, 1001)-Net over F₄ — Digital

Digital (124, 172, 1001)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+48, 67434)-Net in Base 4 — Upper bound on s

There is no (124, 172, 67435)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 848118 502583 452757 210402 013142 492783 306891 739771 025605 029028 386968 296537 626109 017894 156936 438560 472094 > 4¹⁷² [i]