MinT - Best Known (52, 52+24, s)-Nets in Base 16

Best Known (52, 52+24, s)-Nets in Base 16

(52, 52+24, 1032)-Net over F₁₆ — Constructive and digital

Digital (52, 76, 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 (26, 50, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 25, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(52, 52+24, 5998)-Net over F₁₆ — Digital

Digital (52, 76, 5998)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+24, large)-Net in Base 16 — Upper bound on s

There is no (52, 76, large)-net in base 16, because

22 times m-reduction [i] would yield (52, 54, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]