MinT - Best Known (157, 223, s)-Nets in Base 4

Best Known (157, 223, s)-Nets in Base 4

(157, 223, 531)-Net over F₄ — Constructive and digital

Digital (157, 223, 531)-net over F₄, using

2 times m-reduction [i] based on digital (157, 225, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 75, 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]

(157, 223, 963)-Net over F₄ — Digital

Digital (157, 223, 963)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 223, 51341)-Net in Base 4 — Upper bound on s

There is no (157, 223, 51342)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 740146 850608 977554 844750 030391 686723 887162 434474 801948 743918 964547 084478 611615 093638 228259 502346 903380 660348 500087 824141 286920 981572 > 4²²³ [i]