MinT - Best Known (134−40, 134, s)-Nets in Base 4

Best Known (134−40, 134, s)-Nets in Base 4

(134−40, 134, 312)-Net over F₄ — Constructive and digital

Digital (94, 134, 312)-net over F₄, using

t-expansion [i] based on digital (93, 134, 312)-net over F₄, using
- 1 times m-reduction [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]

(134−40, 134, 614)-Net over F₄ — Digital

Digital (94, 134, 614)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−40, 134, 29905)-Net in Base 4 — Upper bound on s

There is no (94, 134, 29906)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 474 417007 667432 606544 260960 657748 433540 051953 536981 219839 239724 147282 029656 688784 > 4¹³⁴ [i]