MinT - Best Known (230−73, 230, s)-Nets in Base 4

Best Known (230−73, 230, s)-Nets in Base 4

(230−73, 230, 450)-Net over F₄ — Constructive and digital

Digital (157, 230, 450)-net over F₄, using

4 times m-reduction [i] based on digital (157, 234, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 117, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(230−73, 230, 747)-Net over F₄ — Digital

Digital (157, 230, 747)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−73, 230, 32135)-Net in Base 4 — Upper bound on s

There is no (157, 230, 32136)-net in base 4, because

1 times m-reduction [i] would yield (157, 229, 32136)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744519 400170 142601 559772 237957 506211 409997 496850 286801 787595 801487 610456 360064 841859 630026 127939 895692 738683 811043 622776 408970 503113 082428 > 4²²⁹ [i]