MinT - Best Known (169−74, 169, s)-Nets in Base 4

Best Known (169−74, 169, s)-Nets in Base 4

(169−74, 169, 130)-Net over F₄ — Constructive and digital

Digital (95, 169, 130)-net over F₄, using

9 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(169−74, 169, 189)-Net over F₄ — Digital

Digital (95, 169, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−74, 169, 2716)-Net in Base 4 — Upper bound on s

There is no (95, 169, 2717)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 567182 144151 150804 554281 868145 634126 638037 178444 799937 900978 801767 385112 004506 524655 183327 248299 586960 > 4¹⁶⁹ [i]