MinT - Best Known (107−41, 107, s)-Nets in Base 32

Best Known (107−41, 107, s)-Nets in Base 32

(107−41, 107, 360)-Net over F₃₂ — Constructive and digital

Digital (66, 107, 360)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (11, 24, 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]
2. digital (11, 31, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)
3. digital (11, 52, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(107−41, 107, 578)-Net in Base 32 — Constructive

(66, 107, 578)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (4, 24, 65)-net in base 32, using
  - base change [i] based on digital (0, 20, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
2. (42, 83, 513)-net in base 32, using
  - 1 times m-reduction [i] based on (42, 84, 513)-net in base 32, using
    - base change [i] based on digital (28, 70, 513)-net over F₆₄, using
      - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(107−41, 107, 5424)-Net over F₃₂ — Digital

Digital (66, 107, 5424)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−41, 107, large)-Net in Base 32 — Upper bound on s

There is no (66, 107, large)-net in base 32, because

39 times m-reduction [i] would yield (66, 68, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]