MinT - Best Known (23, 110, s)-Nets in Base 32

Best Known (23, 110, s)-Nets in Base 32

(23, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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, 110, 185)-Net over F₃₂ — Digital

Digital (23, 110, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 110, 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, 110, 3537)-Net in Base 32 — Upper bound on s

There is no (23, 110, 3538)-net in base 32, because

1 times m-reduction [i] would yield (23, 109, 3538)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 246833 706440 657209 500499 464833 823871 496724 705481 051573 695532 382186 917512 853152 621153 596194 267183 946743 263822 927977 713003 027830 319046 530543 588382 975629 451063 169552 > 32¹⁰⁹ [i]