MinT - Best Known (87−70, 87, s)-Nets in Base 32

Best Known (87−70, 87, s)-Nets in Base 32

(87−70, 87, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 87, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 87, 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]

(87−70, 87, 158)-Net over F₃₂ — Digital

Digital (17, 87, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 87, 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]

(87−70, 87, 2455)-Net in Base 32 — Upper bound on s

There is no (17, 87, 2456)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 89749 722619 570707 810680 003298 310974 453208 384258 752508 936261 395053 403858 964875 354233 911392 279070 830569 528119 644286 053646 771365 079660 > 32⁸⁷ [i]