MinT - Best Known (206−58, 206, s)-Nets in Base 4

Best Known (206−58, 206, s)-Nets in Base 4

(206−58, 206, 531)-Net over F₄ — Constructive and digital

Digital (148, 206, 531)-net over F₄, using

t-expansion [i] based on digital (147, 206, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 70, 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]

(206−58, 206, 1116)-Net over F₄ — Digital

Digital (148, 206, 1116)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−58, 206, 73546)-Net in Base 4 — Upper bound on s

There is no (148, 206, 73547)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10578 232730 465023 156279 692992 812708 975853 874391 588151 447478 235774 803472 361203 965522 849442 900344 876473 624561 281870 141711 971808 > 4²⁰⁶ [i]