MinT - Best Known (58−18, 58, s)-Nets in Base 16

Best Known (58−18, 58, s)-Nets in Base 16

(58−18, 58, 1032)-Net over F₁₆ — Constructive and digital

Digital (40, 58, 1032)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (11, 20, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 10, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (20, 38, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 19, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(58−18, 58, 6146)-Net over F₁₆ — Digital

Digital (40, 58, 6146)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(58−18, 58, large)-Net in Base 16 — Upper bound on s

There is no (40, 58, large)-net in base 16, because

16 times m-reduction [i] would yield (40, 42, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]