MinT - Best Known (66, 66+25, s)-Nets in Base 16

Best Known (66, 66+25, s)-Nets in Base 16

(66, 66+25, 1542)-Net over F₁₆ — Constructive and digital

Digital (66, 91, 1542)-net over F₁₆, using

16¹ times duplication [i] based on digital (65, 90, 1542)-net over F₁₆, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (8, 16, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 8, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
  2. digital (12, 24, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 12, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
  3. digital (25, 50, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 25, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(66, 66+25, 24050)-Net over F₁₆ — Digital

Digital (66, 91, 24050)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+25, large)-Net in Base 16 — Upper bound on s

There is no (66, 91, large)-net in base 16, because

23 times m-reduction [i] would yield (66, 68, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]