MinT - Best Known (65, 65+29, s)-Nets in Base 16

Best Known (65, 65+29, s)-Nets in Base 16

(65, 65+29, 1036)-Net over F₁₆ — Constructive and digital

Digital (65, 94, 1036)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (18, 32, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 16, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (33, 62, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 31, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(65, 65+29, 8318)-Net over F₁₆ — Digital

Digital (65, 94, 8318)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+29, large)-Net in Base 16 — Upper bound on s

There is no (65, 94, large)-net in base 16, because

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