MinT - Best Known (100−39, 100, s)-Nets in Base 32

Best Known (100−39, 100, s)-Nets in Base 32

(100−39, 100, 338)-Net over F₃₂ — Constructive and digital

Digital (61, 100, 338)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 20, 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 (11, 30, 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]
3. digital (11, 50, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(100−39, 100, 546)-Net in Base 32 — Constructive

(61, 100, 546)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (13, 32, 258)-net in base 32, using
  - base change [i] based on digital (1, 20, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. (29, 68, 288)-net in base 32, using
  - 2 times m-reduction [i] based on (29, 70, 288)-net in base 32, using
    - base change [i] based on digital (9, 50, 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]

(100−39, 100, 4449)-Net over F₃₂ — Digital

Digital (61, 100, 4449)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−39, 100, large)-Net in Base 32 — Upper bound on s

There is no (61, 100, large)-net in base 32, because

37 times m-reduction [i] would yield (61, 63, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]