MinT - Best Known (6, 6+23, s)-Nets in Base 32

Best Known (6, 6+23, s)-Nets in Base 32

(6, 6+23, 76)-Net over F₃₂ — Constructive and digital

Digital (6, 29, 76)-net over F₃₂, using

t-expansion [i] based on digital (5, 29, 76)-net over F₃₂, using
- net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(6, 6+23, 80)-Net in Base 32 — Constructive

(6, 29, 80)-net in base 32, using

1 times m-reduction [i] based on (6, 30, 80)-net in base 32, using
- base change [i] based on digital (1, 25, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(6, 6+23, 86)-Net over F₃₂ — Digital

Digital (6, 29, 86)-net over F₃₂, using

net from sequence [i] based on digital (6, 85)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 6 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(6, 6+23, 1068)-Net in Base 32 — Upper bound on s

There is no (6, 29, 1069)-net in base 32, because

1 times m-reduction [i] would yield (6, 28, 1069)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 400941 006923 254575 394233 582702 291341 901380 > 32²⁸ [i]