MinT - Best Known (127−40, 127, s)-Nets in Base 16

Best Known (127−40, 127, s)-Nets in Base 16

(127−40, 127, 1034)-Net over F₁₆ — Constructive and digital

Digital (87, 127, 1034)-net over F₁₆, using

1 times m-reduction [i] based on digital (87, 128, 1034)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (22, 42, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 21, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (45, 86, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 43, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(127−40, 127, 8579)-Net over F₁₆ — Digital

Digital (87, 127, 8579)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−40, 127, large)-Net in Base 16 — Upper bound on s

There is no (87, 127, large)-net in base 16, because

38 times m-reduction [i] would yield (87, 89, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]