MinT - Best Known (53, 53+33, s)-Nets in Base 32

Best Known (53, 53+33, s)-Nets in Base 32

(53, 53+33, 316)-Net over F₃₂ — Constructive and digital

Digital (53, 86, 316)-net over F₃₂, using

2 times m-reduction [i] based on digital (53, 88, 316)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 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, 24, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (11, 46, 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]

(53, 53+33, 518)-Net in Base 32 — Constructive

(53, 86, 518)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (14, 30, 259)-net in base 32, using
  - 2 times m-reduction [i] based on (14, 32, 259)-net in base 32, using
    - base change [i] based on digital (2, 20, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. (23, 56, 259)-net in base 32, using
  - base change [i] based on digital (2, 35, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(53, 53+33, 4593)-Net over F₃₂ — Digital

Digital (53, 86, 4593)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+33, large)-Net in Base 32 — Upper bound on s

There is no (53, 86, large)-net in base 32, because

31 times m-reduction [i] would yield (53, 55, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]