MinT - Best Known (88−74, 88, s)-Nets in Base 32

Best Known (88−74, 88, s)-Nets in Base 32

(88−74, 88, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 88, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 88, 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]

(88−74, 88, 146)-Net over F₃₂ — Digital

Digital (14, 88, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(88−74, 88, 1777)-Net in Base 32 — Upper bound on s

There is no (14, 88, 1778)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 892425 046729 074000 079751 785980 071611 139631 671100 406537 506636 258659 363602 248102 537978 045180 386673 492672 388986 599735 379922 854863 859796 > 32⁸⁸ [i]