MinT - Best Known (213−63, 213, s)-Nets in Base 4

Best Known (213−63, 213, s)-Nets in Base 4

(213−63, 213, 531)-Net over F₄ — Constructive and digital

Digital (150, 213, 531)-net over F₄, using

t-expansion [i] based on digital (149, 213, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 71, 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]

(213−63, 213, 928)-Net over F₄ — Digital

Digital (150, 213, 928)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−63, 213, 54202)-Net in Base 4 — Upper bound on s

There is no (150, 213, 54203)-net in base 4, because

1 times m-reduction [i] would yield (150, 212, 54203)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 326136 471757 324632 997045 525607 260478 723063 243458 784288 300827 919680 502546 248934 399784 580608 447340 215923 709604 874782 052249 252160 > 4²¹² [i]