MinT - Best Known (42, 68, s)-Nets in Base 32

Best Known (42, 68, s)-Nets in Base 32

(42, 68, 294)-Net over F₃₂ — Constructive and digital

Digital (42, 68, 294)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 15, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (7, 20, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
3. digital (7, 33, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(42, 68, 517)-Net in Base 32 — Constructive

(42, 68, 517)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (8, 21, 257)-net in base 32, using
  - base change [i] based on (2, 15, 257)-net in base 128, using
    - 1 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
      - base change [i] based on digital (0, 14, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
2. (21, 47, 260)-net in base 32, using
  - 1 times m-reduction [i] based on (21, 48, 260)-net in base 32, using
    - base change [i] based on digital (3, 30, 260)-net over F₂₅₆, using
      - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(42, 68, 4089)-Net over F₃₂ — Digital

Digital (42, 68, 4089)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 68, large)-Net in Base 32 — Upper bound on s

There is no (42, 68, large)-net in base 32, because

24 times m-reduction [i] would yield (42, 44, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]