MinT - Best Known (84, 84+38, s)-Nets in Base 16

Best Known (84, 84+38, s)-Nets in Base 16

(84, 84+38, 1036)-Net over F₁₆ — Constructive and digital

Digital (84, 122, 1036)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (23, 42, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 21, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (42, 80, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 40, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(84, 84+38, 9142)-Net over F₁₆ — Digital

Digital (84, 122, 9142)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+38, large)-Net in Base 16 — Upper bound on s

There is no (84, 122, large)-net in base 16, because

36 times m-reduction [i] would yield (84, 86, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]