MinT - Best Known (133−37, 133, s)-Nets in Base 4

Best Known (133−37, 133, s)-Nets in Base 4

(133−37, 133, 531)-Net over F₄ — Constructive and digital

Digital (96, 133, 531)-net over F₄, using

4¹ times duplication [i] based on digital (95, 132, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 44, 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]

(133−37, 133, 816)-Net over F₄ — Digital

Digital (96, 133, 816)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−37, 133, 65466)-Net in Base 4 — Upper bound on s

There is no (96, 133, 65467)-net in base 4, because

1 times m-reduction [i] would yield (96, 132, 65467)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 646714 035536 861778 952084 302117 490540 895106 695617 194327 433372 061906 782192 958501 > 4¹³² [i]