MinT - Best Known (165−72, 165, s)-Nets in Base 4

Best Known (165−72, 165, s)-Nets in Base 4

(165−72, 165, 130)-Net over F₄ — Constructive and digital

Digital (93, 165, 130)-net over F₄, using

9 times m-reduction [i] based on digital (93, 174, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 87, 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]

(165−72, 165, 187)-Net over F₄ — Digital

Digital (93, 165, 187)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−72, 165, 2706)-Net in Base 4 — Upper bound on s

There is no (93, 165, 2707)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2208 884506 693790 500016 592704 870953 993793 838521 090761 709107 040101 918759 326799 071205 812353 646634 463920 > 4¹⁶⁵ [i]