MinT - Best Known (31, 66, s)-Nets in Base 256

Best Known (31, 66, s)-Nets in Base 256

(31, 66, 774)-Net over F₂₅₆ — Constructive and digital

Digital (31, 66, 774)-net over F₂₅₆, using

generalized (u,Â u+v)-construction [i] based on
1. 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 (1, 18, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)
3. digital (1, 36, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(31, 66, 2527)-Net over F₂₅₆ — Digital

Digital (31, 66, 2527)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(31, 66, large)-Net in Base 256 — Upper bound on s

There is no (31, 66, large)-net in base 256, because

33 times m-reduction [i] would yield (31, 33, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]