MinT - Best Known (76, 76+34, s)-Nets in Base 16

Best Known (76, 76+34, s)-Nets in Base 16

(76, 76+34, 1036)-Net over F₁₆ — Constructive and digital

Digital (76, 110, 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 (38, 72, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 36, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(76, 76+34, 9074)-Net over F₁₆ — Digital

Digital (76, 110, 9074)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+34, large)-Net in Base 16 — Upper bound on s

There is no (76, 110, large)-net in base 16, because

32 times m-reduction [i] would yield (76, 78, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]