MinT - Best Known (230−70, 230, s)-Nets in Base 4

Best Known (230−70, 230, s)-Nets in Base 4

(230−70, 230, 450)-Net over F₄ — Constructive and digital

Digital (160, 230, 450)-net over F₄, using

10 times m-reduction [i] based on digital (160, 240, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 120, 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]

(230−70, 230, 882)-Net over F₄ — Digital

Digital (160, 230, 882)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−70, 230, 41902)-Net in Base 4 — Upper bound on s

There is no (160, 230, 41903)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 978399 200877 714664 539330 005865 334325 496501 714024 039445 805046 597594 146958 959088 568579 596134 118372 757558 362583 519848 693433 047610 844800 705832 > 4²³⁰ [i]