MinT - Best Known (96−81, 96, s)-Nets in Base 32

Best Known (96−81, 96, s)-Nets in Base 32

(96−81, 96, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 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]

(96−81, 96, 158)-Net over F₃₂ — Digital

Digital (15, 96, 158)-net over F₃₂, using

net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
  - an algebraic function field by Beelen and Pellikaan [i]

(96−81, 96, 1889)-Net in Base 32 — Upper bound on s

There is no (15, 96, 1890)-net in base 32, because

1 times m-reduction [i] would yield (15, 95, 1890)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 97927 412660 010892 271941 075355 797840 521282 530921 343701 584107 670806 251646 452253 312395 304678 394631 588520 020011 189303 907218 934172 983048 479366 946696 > 32⁹⁵ [i]