MinT - Best Known (61, 61+28, s)-Nets in Base 16

Best Known (61, 61+28, s)-Nets in Base 16

(61, 61+28, 1032)-Net over F₁₆ — Constructive and digital

Digital (61, 89, 1032)-net over F₁₆, using

1 times m-reduction [i] based on digital (61, 90, 1032)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (16, 30, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 15, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (31, 60, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 30, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(61, 61+28, 6797)-Net over F₁₆ — Digital

Digital (61, 89, 6797)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+28, large)-Net in Base 16 — Upper bound on s

There is no (61, 89, large)-net in base 16, because

26 times m-reduction [i] would yield (61, 63, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]