MinT - Best Known (47, 77, s)-Nets in Base 32

Best Known (47, 77, s)-Nets in Base 32

(47, 77, 294)-Net over F₃₂ — Constructive and digital

Digital (47, 77, 294)-net over F₃₂, using

2 times m-reduction [i] based on digital (47, 79, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 17, 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, 23, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 39, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(47, 77, 517)-Net in Base 32 — Constructive

(47, 77, 517)-net in base 32, using

base change [i] based on (25, 55, 517)-net in base 128, using
- 1 times m-reduction [i] based on (25, 56, 517)-net in base 128, using
  - base change [i] based on digital (18, 49, 517)-net over F₂₅₆, using
    - (u,Â u+v)-construction [i] based on
      1. digital (1, 16, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
      2. digital (2, 33, 259)-net over F₂₅₆, using
        net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(47, 77, 3749)-Net over F₃₂ — Digital

Digital (47, 77, 3749)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 77, large)-Net in Base 32 — Upper bound on s

There is no (47, 77, large)-net in base 32, because

28 times m-reduction [i] would yield (47, 49, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]