MinT - Best Known (165−74, 165, s)-Nets in Base 4

Best Known (165−74, 165, s)-Nets in Base 4

(165−74, 165, 130)-Net over F₄ — Constructive and digital

Digital (91, 165, 130)-net over F₄, using

5 times m-reduction [i] based on digital (91, 170, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 85, 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]

(165−74, 165, 171)-Net over F₄ — Digital

Digital (91, 165, 171)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−74, 165, 2333)-Net in Base 4 — Upper bound on s

There is no (91, 165, 2334)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2192 621897 538702 609667 833235 064243 214443 856802 475802 473726 077090 032909 914423 382944 389388 526057 913960 > 4¹⁶⁵ [i]