MinT - Best Known (50, 50+29, s)-Nets in Base 32

Best Known (50, 50+29, s)-Nets in Base 32

(50, 50+29, 324)-Net over F₃₂ — Constructive and digital

Digital (50, 79, 324)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (3, 10, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (3, 12, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂ (see above)
3. digital (7, 21, 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]
4. digital (7, 36, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(50, 50+29, 546)-Net in Base 32 — Constructive

(50, 79, 546)-net in base 32, using

32¹ times duplication [i] based on (49, 78, 546)-net in base 32, using
- (u,Â u+v)-construction [i] based on
  1. (10, 24, 258)-net in base 32, using
    - base change [i] based on digital (1, 15, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. (25, 54, 288)-net in base 32, using
    - 2 times m-reduction [i] based on (25, 56, 288)-net in base 32, using
      - base change [i] based on digital (9, 40, 288)-net over F₁₂₈, using
        net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(50, 50+29, 6446)-Net over F₃₂ — Digital

Digital (50, 79, 6446)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+29, large)-Net in Base 32 — Upper bound on s

There is no (50, 79, large)-net in base 32, because

27 times m-reduction [i] would yield (50, 52, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]