MinT - Best Known (15, 15+72, s)-Nets in Base 32

Best Known (15, 15+72, s)-Nets in Base 32

(15, 15+72, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 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]

(15, 15+72, 158)-Net over F₃₂ — Digital

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]

(15, 15+72, 1980)-Net in Base 32 — Upper bound on s

There is no (15, 87, 1981)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 89665 450694 607953 604864 748410 255151 893599 220910 157974 373348 480916 138264 637166 420430 410608 019712 226033 877282 126748 149618 310860 087181 > 32⁸⁷ [i]