MinT - Best Known (83, 83+37, s)-Nets in Base 16

Best Known (83, 83+37, s)-Nets in Base 16

(83, 83+37, 1038)-Net over F₁₆ — Constructive and digital

Digital (83, 120, 1038)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (22, 40, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 20, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (43, 80, 520)-net over F₁₆, using
  - trace code for nets [i] based on digital (3, 40, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(83, 83+37, 9844)-Net over F₁₆ — Digital

Digital (83, 120, 9844)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+37, large)-Net in Base 16 — Upper bound on s

There is no (83, 120, large)-net in base 16, because

35 times m-reduction [i] would yield (83, 85, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]