MinT - Best Known (68−38, 68, s)-Nets in Base 256

Best Known (68−38, 68, s)-Nets in Base 256

(68−38, 68, 525)-Net over F₂₅₆ — Constructive and digital

Digital (30, 68, 525)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (5, 24, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (6, 44, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(68−38, 68, 1551)-Net over F₂₅₆ — Digital

Digital (30, 68, 1551)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(68−38, 68, large)-Net in Base 256 — Upper bound on s

There is no (30, 68, large)-net in base 256, because

36 times m-reduction [i] would yield (30, 32, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]