MinT - Best Known (17, 17+86, s)-Nets in Base 32

Best Known (17, 17+86, s)-Nets in Base 32

(17, 17+86, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 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+86, 158)-Net over F₃₂ — Digital

Digital (17, 103, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 103, 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+86, 2172)-Net in Base 32 — Upper bound on s

There is no (17, 103, 2173)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107639 006062 029733 106707 108709 716536 109259 707005 862642 047345 082825 716538 543662 299313 574456 904847 587199 997127 554495 836200 200045 527285 056407 961630 379622 512444 > 32¹⁰³ [i]