MinT - Best Known (124−39, 124, s)-Nets in Base 16

Best Known (124−39, 124, s)-Nets in Base 16

(124−39, 124, 1036)-Net over F₁₆ — Constructive and digital

Digital (85, 124, 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 (43, 82, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 41, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(124−39, 124, 8529)-Net over F₁₆ — Digital

Digital (85, 124, 8529)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−39, 124, large)-Net in Base 16 — Upper bound on s

There is no (85, 124, large)-net in base 16, because

37 times m-reduction [i] would yield (85, 87, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]