MinT - Best Known (69, 69+30, s)-Nets in Base 16

Best Known (69, 69+30, s)-Nets in Base 16

(69, 69+30, 1036)-Net over F₁₆ — Constructive and digital

Digital (69, 99, 1036)-net over F₁₆, using

1 times m-reduction [i] based on digital (69, 100, 1036)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (19, 34, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 17, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (35, 66, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 33, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(69, 69+30, 10052)-Net over F₁₆ — Digital

Digital (69, 99, 10052)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+30, large)-Net in Base 16 — Upper bound on s

There is no (69, 99, large)-net in base 16, because

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