MinT - Best Known (53, 77, s)-Nets in Base 16

Best Known (53, 77, s)-Nets in Base 16

(53, 77, 1032)-Net over F₁₆ — Constructive and digital

Digital (53, 77, 1032)-net over F₁₆, using

1 times m-reduction [i] based on digital (53, 78, 1032)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 26, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 13, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (27, 52, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 26, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(53, 77, 6765)-Net over F₁₆ — Digital

Digital (53, 77, 6765)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 77, large)-Net in Base 16 — Upper bound on s

There is no (53, 77, large)-net in base 16, because

22 times m-reduction [i] would yield (53, 55, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]