MinT - Best Known (22, 22+85, s)-Nets in Base 32

Best Known (22, 22+85, s)-Nets in Base 32

(22, 22+85, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 107, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 107, 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]

(22, 22+85, 185)-Net over F₃₂ — Digital

Digital (22, 107, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 107, 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]

(22, 22+85, 3329)-Net in Base 32 — Upper bound on s

There is no (22, 107, 3330)-net in base 32, because

1 times m-reduction [i] would yield (22, 106, 3330)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3558 982034 455082 939558 746404 882994 936782 571490 320476 443556 844783 669399 570594 058864 518486 619370 287116 169882 862295 019391 305635 821926 241199 921339 857554 628864 668800 > 32¹⁰⁶ [i]