MinT - Best Known (25, 58, s)-Nets in Base 256

Best Known (25, 58, s)-Nets in Base 256

(25, 58, 523)-Net over F₂₅₆ — Constructive and digital

Digital (25, 58, 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, 38, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(25, 58, 1178)-Net over F₂₅₆ — Digital

Digital (25, 58, 1178)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(25, 58, large)-Net in Base 256 — Upper bound on s

There is no (25, 58, large)-net in base 256, because

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