MinT - Best Known (129, 129+47, s)-Nets in Base 4

Best Known (129, 129+47, s)-Nets in Base 4

(129, 129+47, 531)-Net over F₄ — Constructive and digital

Digital (129, 176, 531)-net over F₄, using

7 times m-reduction [i] based on digital (129, 183, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 61, 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]

(129, 129+47, 1230)-Net over F₄ — Digital

Digital (129, 176, 1230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 129+47, 119717)-Net in Base 4 — Upper bound on s

There is no (129, 176, 119718)-net in base 4, because

1 times m-reduction [i] would yield (129, 175, 119718)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2293 607509 106114 407290 457556 122114 017497 326083 442724 577965 784739 688355 652960 538348 556688 409494 121270 208400 > 4¹⁷⁵ [i]