MinT - Best Known (108−35, 108, s)-Nets in Base 16

Best Known (108−35, 108, s)-Nets in Base 16

(108−35, 108, 1032)-Net over F₁₆ — Constructive and digital

Digital (73, 108, 1032)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (19, 36, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 18, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (37, 72, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 36, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(108−35, 108, 6046)-Net over F₁₆ — Digital

Digital (73, 108, 6046)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−35, 108, large)-Net in Base 16 — Upper bound on s

There is no (73, 108, large)-net in base 16, because

33 times m-reduction [i] would yield (73, 75, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]