MinT - Best Known (17, 96, s)-Nets in Base 32

Best Known (17, 96, s)-Nets in Base 32

(17, 96, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 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]

(17, 96, 158)-Net over F₃₂ — Digital

Digital (17, 96, 158)-net over F₃₂, using

t-expansion [i] based on 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]

(17, 96, 2283)-Net in Base 32 — Upper bound on s

There is no (17, 96, 2284)-net in base 32, because

1 times m-reduction [i] would yield (17, 95, 2284)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 98164 443187 665754 797256 512411 117793 528227 944584 924852 772728 954585 506284 964156 388975 079509 910937 799560 185810 300792 451577 107902 112685 955048 755338 > 32⁹⁵ [i]