MinT - Best Known (69, 69+33, s)-Nets in Base 16

Best Known (69, 69+33, s)-Nets in Base 16

(69, 69+33, 1032)-Net over F₁₆ — Constructive and digital

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+33, 5890)-Net over F₁₆ — Digital

Digital (69, 102, 5890)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+33, large)-Net in Base 16 — Upper bound on s

There is no (69, 102, large)-net in base 16, because

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