MinT - Best Known (54−30, 54, s)-Nets in Base 256

Best Known (54−30, 54, s)-Nets in Base 256

(54−30, 54, 523)-Net over F₂₅₆ — Constructive and digital

Digital (24, 54, 523)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (4, 19, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (5, 35, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(54−30, 54, 1411)-Net over F₂₅₆ — Digital

Digital (24, 54, 1411)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−30, 54, large)-Net in Base 256 — Upper bound on s

There is no (24, 54, large)-net in base 256, because

28 times m-reduction [i] would yield (24, 26, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]