MinT - Best Known (210−59, 210, s)-Nets in Base 4

Best Known (210−59, 210, s)-Nets in Base 4

(210−59, 210, 531)-Net over F₄ — Constructive and digital

Digital (151, 210, 531)-net over F₄, using

6 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 72, 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]

(210−59, 210, 1145)-Net over F₄ — Digital

Digital (151, 210, 1145)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−59, 210, 84891)-Net in Base 4 — Upper bound on s

There is no (151, 210, 84892)-net in base 4, because

1 times m-reduction [i] would yield (151, 209, 84892)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 677055 193638 754598 077379 065241 030729 058970 650082 056732 497167 621607 812467 754155 847959 897952 317299 675407 672730 841627 024751 733056 > 4²⁰⁹ [i]