MinT - Best Known (17, 17+59, s)-Nets in Base 32

Best Known (17, 17+59, s)-Nets in Base 32

(17, 17+59, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 76, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 76, 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, 17+59, 158)-Net over F₃₂ — Digital

Digital (17, 76, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 76, 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, 17+59, 2925)-Net in Base 32 — Upper bound on s

There is no (17, 76, 2926)-net in base 32, because

1 times m-reduction [i] would yield (17, 75, 2926)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 77438 892962 740153 604193 282228 501990 909264 571046 367490 143645 459700 077814 620339 611625 939235 917903 772453 056182 391074 > 32⁷⁵ [i]