MinT - Best Known (168−74, 168, s)-Nets in Base 4

Best Known (168−74, 168, s)-Nets in Base 4

(168−74, 168, 130)-Net over F₄ — Constructive and digital

Digital (94, 168, 130)-net over F₄, using

8 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(168−74, 168, 184)-Net over F₄ — Digital

Digital (94, 168, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−74, 168, 2615)-Net in Base 4 — Upper bound on s

There is no (94, 168, 2616)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 141838 033118 845269 245571 767620 743273 549341 866214 688815 516867 684391 221836 036485 946215 896129 170172 211265 > 4¹⁶⁸ [i]