MinT - Best Known (79, 79+35, s)-Nets in Base 16

Best Known (79, 79+35, s)-Nets in Base 16

(79, 79+35, 1038)-Net over F₁₆ — Constructive and digital

Digital (79, 114, 1038)-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 (41, 76, 520)-net over F₁₆, using
  - trace code for nets [i] based on digital (3, 38, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(79, 79+35, 9851)-Net over F₁₆ — Digital

Digital (79, 114, 9851)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+35, large)-Net in Base 16 — Upper bound on s

There is no (79, 114, large)-net in base 16, because

33 times m-reduction [i] would yield (79, 81, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]