MinT - Best Known (248−84, 248, s)-Nets in Base 4

Best Known (248−84, 248, s)-Nets in Base 4

(248−84, 248, 450)-Net over F₄ — Constructive and digital

Digital (164, 248, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 124, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(248−84, 248, 628)-Net over F₄ — Digital

Digital (164, 248, 628)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−84, 248, 19721)-Net in Base 4 — Upper bound on s

There is no (164, 248, 19722)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 204745 119051 960886 873894 872123 534203 218250 728608 564811 017245 571073 307076 231878 554913 385868 973045 131381 786870 465822 500642 560722 105414 586404 535437 449280 > 4²⁴⁸ [i]