MinT - Best Known (57−32, 57, s)-Nets in Base 256

Best Known (57−32, 57, s)-Nets in Base 256

(57−32, 57, 523)-Net over F₂₅₆ — Constructive and digital

Digital (25, 57, 523)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (4, 20, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (5, 37, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(57−32, 57, 1320)-Net over F₂₅₆ — Digital

Digital (25, 57, 1320)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−32, 57, large)-Net in Base 256 — Upper bound on s

There is no (25, 57, large)-net in base 256, because

30 times m-reduction [i] would yield (25, 27, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]