MinT - Best Known (69, 69+32, s)-Nets in Base 16

Best Known (69, 69+32, s)-Nets in Base 16

(69, 69+32, 1032)-Net over F₁₆ — Constructive and digital

Digital (69, 101, 1032)-net over F₁₆, using

1 times m-reduction [i] based on digital (69, 102, 1032)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (18, 34, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 17, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (35, 68, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 34, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(69, 69+32, 6950)-Net over F₁₆ — Digital

Digital (69, 101, 6950)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+32, large)-Net in Base 16 — Upper bound on s

There is no (69, 101, large)-net in base 16, because

30 times m-reduction [i] would yield (69, 71, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]