MinT - Best Known (112−35, 112, s)-Nets in Base 16

Best Known (112−35, 112, s)-Nets in Base 16

(112−35, 112, 1036)-Net over F₁₆ — Constructive and digital

Digital (77, 112, 1036)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (21, 38, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 19, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (39, 74, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 37, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(112−35, 112, 8371)-Net over F₁₆ — Digital

Digital (77, 112, 8371)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−35, 112, large)-Net in Base 16 — Upper bound on s

There is no (77, 112, large)-net in base 16, because

33 times m-reduction [i] would yield (77, 79, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]