MinT - Best Known (55, 91, s)-Nets in Base 32

Best Known (55, 91, s)-Nets in Base 32

(55, 91, 316)-Net over F₃₂ — Constructive and digital

Digital (55, 91, 316)-net over F₃₂, using

1 times m-reduction [i] based on digital (55, 92, 316)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 19, 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, 25, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (11, 48, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(55, 91, 516)-Net in Base 32 — Constructive

(55, 91, 516)-net in base 32, using

32¹ times duplication [i] based on (54, 90, 516)-net in base 32, using
- base change [i] based on (39, 75, 516)-net in base 64, using
  - 1 times m-reduction [i] based on (39, 76, 516)-net in base 64, using
    - base change [i] based on digital (20, 57, 516)-net over F₂₅₆, using
      - (u,Â u+v)-construction [i] based on
        digital (1, 19, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
        digital (1, 38, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(55, 91, 3693)-Net over F₃₂ — Digital

Digital (55, 91, 3693)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 91, large)-Net in Base 32 — Upper bound on s

There is no (55, 91, large)-net in base 32, because

34 times m-reduction [i] would yield (55, 57, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]