MinT - Best Known (52, 52+33, s)-Nets in Base 32

Best Known (52, 52+33, s)-Nets in Base 32

(52, 52+33, 316)-Net over F₃₂ — Constructive and digital

Digital (52, 85, 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, 23, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
3. digital (11, 44, 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]

(52, 52+33, 517)-Net in Base 32 — Constructive

(52, 85, 517)-net in base 32, using

32¹ times duplication [i] based on (51, 84, 517)-net in base 32, using
- (u,Â u+v)-construction [i] based on
  1. (12, 28, 258)-net in base 32, using
    - base change [i] based on (4, 20, 258)-net in base 128, using
      - 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
        base change [i] based on digital (1, 21, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-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, using
        Niederreiter sequence [i]

(52, 52+33, 4123)-Net over F₃₂ — Digital

Digital (52, 85, 4123)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+33, large)-Net in Base 32 — Upper bound on s

There is no (52, 85, large)-net in base 32, because

31 times m-reduction [i] would yield (52, 54, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]