MinT - Best Known (65, 65+31, s)-Nets in Base 16

Best Known (65, 65+31, s)-Nets in Base 16

(65, 65+31, 1032)-Net over F₁₆ — Constructive and digital

Digital (65, 96, 1032)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (17, 32, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 16, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (33, 64, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 32, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(65, 65+31, 5741)-Net over F₁₆ — Digital

Digital (65, 96, 5741)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+31, large)-Net in Base 16 — Upper bound on s

There is no (65, 96, large)-net in base 16, because

29 times m-reduction [i] would yield (65, 67, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]