MinT - Best Known (86−69, 86, s)-Nets in Base 32

Best Known (86−69, 86, s)-Nets in Base 32

(86−69, 86, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 86, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 86, 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]

(86−69, 86, 158)-Net over F₃₂ — Digital

Digital (17, 86, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 86, 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]

(86−69, 86, 2511)-Net in Base 32 — Upper bound on s

There is no (17, 86, 2512)-net in base 32, because

1 times m-reduction [i] would yield (17, 85, 2512)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 87 040860 061596 180918 846332 655855 986058 221383 546006 537294 528741 234237 726338 111304 646679 982518 983333 899328 151149 962829 066331 700114 > 32⁸⁵ [i]