MinT - Best Known (64, 64+28, s)-Nets in Base 16

Best Known (64, 64+28, s)-Nets in Base 16

(64, 64+28, 1036)-Net over F₁₆ — Constructive and digital

Digital (64, 92, 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 (32, 60, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 30, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(64, 64+28, 9244)-Net over F₁₆ — Digital

Digital (64, 92, 9244)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+28, large)-Net in Base 16 — Upper bound on s

There is no (64, 92, large)-net in base 16, because

26 times m-reduction [i] would yield (64, 66, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]