MinT - Best Known (137−43, 137, s)-Nets in Base 4

Best Known (137−43, 137, s)-Nets in Base 4

(137−43, 137, 240)-Net over F₄ — Constructive and digital

Digital (94, 137, 240)-net over F₄, using

t-expansion [i] based on digital (93, 137, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (93, 138, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 46, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(137−43, 137, 506)-Net over F₄ — Digital

Digital (94, 137, 506)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−43, 137, 22914)-Net in Base 4 — Upper bound on s

There is no (94, 137, 22915)-net in base 4, because

1 times m-reduction [i] would yield (94, 136, 22915)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7594 183673 074411 824928 033873 163791 972303 860538 055044 589400 818876 608864 471083 174976 > 4¹³⁶ [i]