MinT - Best Known (213−64, 213, s)-Nets in Base 4

Best Known (213−64, 213, s)-Nets in Base 4

(213−64, 213, 531)-Net over F₄ — Constructive and digital

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]

(213−64, 213, 870)-Net over F₄ — Digital

Digital (149, 213, 870)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−64, 213, 43346)-Net in Base 4 — Upper bound on s

There is no (149, 213, 43347)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 293652 422339 731787 539386 596091 223212 410709 246955 418915 264751 269598 693248 032711 734091 593985 086400 753682 967924 031073 737225 087130 > 4²¹³ [i]