MinT - Best Known (75−52, 75, s)-Nets in Base 32

Best Known (75−52, 75, s)-Nets in Base 32

(75−52, 75, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 75, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 75, 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]

(75−52, 75, 177)-Net in Base 32 — Constructive

(23, 75, 177)-net in base 32, using

21 times m-reduction [i] based on (23, 96, 177)-net in base 32, using
- base change [i] based on digital (7, 80, 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]

(75−52, 75, 185)-Net over F₃₂ — Digital

Digital (23, 75, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 75, 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]

(75−52, 75, 225)-Net in Base 32

(23, 75, 225)-net in base 32, using

3 times m-reduction [i] based on (23, 78, 225)-net in base 32, using
- base change [i] based on digital (10, 65, 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]

(75−52, 75, 7463)-Net in Base 32 — Upper bound on s

There is no (23, 75, 7464)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 77125 954048 119895 203662 450658 468748 532350 875638 528472 182474 498676 202832 996260 032072 167736 084943 064566 867661 000900 > 32⁷⁵ [i]