MinT - Best Known (67−45, 67, s)-Nets in Base 32

Best Known (67−45, 67, s)-Nets in Base 32

(67−45, 67, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 67, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 67, 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]

(67−45, 67, 177)-Net in Base 32 — Constructive

(22, 67, 177)-net in base 32, using

23 times m-reduction [i] based on (22, 90, 177)-net in base 32, using
- base change [i] based on digital (7, 75, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(67−45, 67, 185)-Net over F₃₂ — Digital

Digital (22, 67, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 67, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(67−45, 67, 225)-Net in Base 32

(22, 67, 225)-net in base 32, using

5 times m-reduction [i] based on (22, 72, 225)-net in base 32, using
- base change [i] based on digital (10, 60, 225)-net over F₆₄, using
  - net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
      - a curve from the manYPoints database [i]

(67−45, 67, 9559)-Net in Base 32 — Upper bound on s

There is no (22, 67, 9560)-net in base 32, because

1 times m-reduction [i] would yield (22, 66, 9560)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2190 070228 600950 361134 064107 031981 671844 860557 379354 025529 790478 850684 629664 478536 476000 586824 259403 > 32⁶⁶ [i]