MinT - Best Known (23, 23+73, s)-Nets in Base 32

Best Known (23, 23+73, s)-Nets in Base 32

(23, 23+73, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 96, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 96, 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, 23+73, 177)-Net in Base 32 — Constructive

(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, 23+73, 185)-Net over F₃₂ — Digital

Digital (23, 96, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 96, 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, 23+73, 4299)-Net in Base 32 — Upper bound on s

There is no (23, 96, 4300)-net in base 32, because

1 times m-reduction [i] would yield (23, 95, 4300)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 97947 248939 556686 934336 264100 156780 397664 994223 064690 213569 424429 158668 309816 292759 914623 378368 281187 708710 230678 687688 509241 994051 766511 383988 > 32⁹⁵ [i]