MinT - Best Known (136−42, 136, s)-Nets in Base 4

Best Known (136−42, 136, s)-Nets in Base 4

(136−42, 136, 312)-Net over F₄ — Constructive and digital

Digital (94, 136, 312)-net over F₄, using

4¹ times duplication [i] based on digital (93, 135, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 45, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(136−42, 136, 538)-Net over F₄ — Digital

Digital (94, 136, 538)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−42, 136, 22914)-Net in Base 4 — Upper bound on s

There is no (94, 136, 22915)-net in base 4, because

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]