MinT - Best Known (106−33, 106, s)-Nets in Base 16

Best Known (106−33, 106, s)-Nets in Base 16

(106−33, 106, 1036)-Net over F₁₆ — Constructive and digital

Digital (73, 106, 1036)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (20, 36, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 18, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (37, 70, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 35, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(106−33, 106, 8323)-Net over F₁₆ — Digital

Digital (73, 106, 8323)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−33, 106, large)-Net in Base 16 — Upper bound on s

There is no (73, 106, large)-net in base 16, because

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