MinT - Best Known (23, 84, s)-Nets in Base 32

Best Known (23, 84, s)-Nets in Base 32

(23, 84, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 84, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 84, 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]

(23, 84, 177)-Net in Base 32 — Constructive

(23, 84, 177)-net in base 32, using

12 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]

(23, 84, 185)-Net over F₃₂ — Digital

Digital (23, 84, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 84, 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]

(23, 84, 209)-Net in Base 32

(23, 84, 209)-net in base 32, using

base change [i] based on digital (9, 70, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(23, 84, 5655)-Net in Base 32 — Upper bound on s

There is no (23, 84, 5656)-net in base 32, because

1 times m-reduction [i] would yield (23, 83, 5656)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 84729 315520 670195 351041 056583 782202 399910 636499 481490 851593 561593 647624 682839 886738 700181 626579 504687 690648 049307 596478 637504 > 32⁸³ [i]