MinT - Best Known (137, 137+55, s)-Nets in Base 4

Best Known (137, 137+55, s)-Nets in Base 4

(137, 137+55, 531)-Net over F₄ — Constructive and digital

Digital (137, 192, 531)-net over F₄, using

3 times m-reduction [i] based on digital (137, 195, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 65, 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]

(137, 137+55, 976)-Net over F₄ — Digital

Digital (137, 192, 976)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+55, 66093)-Net in Base 4 — Upper bound on s

There is no (137, 192, 66094)-net in base 4, because

1 times m-reduction [i] would yield (137, 191, 66094)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 852989 128890 057075 633180 849807 310578 898786 258542 126747 729702 743716 646216 581070 755658 853300 186931 698446 995803 883300 > 4¹⁹¹ [i]