MinT - Best Known (51, 51+23, s)-Nets in Base 16

Best Known (51, 51+23, s)-Nets in Base 16

(51, 51+23, 1034)-Net over F₁₆ — Constructive and digital

Digital (51, 74, 1034)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (13, 24, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 12, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (27, 50, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 25, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(51, 51+23, 6787)-Net over F₁₆ — Digital

Digital (51, 74, 6787)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+23, large)-Net in Base 16 — Upper bound on s

There is no (51, 74, large)-net in base 16, because

21 times m-reduction [i] would yield (51, 53, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]