MinT - Best Known (44, 44+20, s)-Nets in Base 16

Best Known (44, 44+20, s)-Nets in Base 16

(44, 44+20, 1032)-Net over F₁₆ — Constructive and digital

Digital (44, 64, 1032)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (12, 22, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 11, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (22, 42, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 21, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(44, 44+20, 6023)-Net over F₁₆ — Digital

Digital (44, 64, 6023)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+20, large)-Net in Base 16 — Upper bound on s

There is no (44, 64, large)-net in base 16, because

18 times m-reduction [i] would yield (44, 46, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]