MinT - Best Known (17, 17+81, s)-Nets in Base 32

Best Known (17, 17+81, s)-Nets in Base 32

(17, 17+81, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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+81, 158)-Net over F₃₂ — Digital

Digital (17, 98, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 98, 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+81, 2251)-Net in Base 32 — Upper bound on s

There is no (17, 98, 2252)-net in base 32, because

1 times m-reduction [i] would yield (17, 97, 2252)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 101 131545 750810 764501 462125 841803 185122 995675 098731 613206 568189 943606 116182 310507 141709 859881 751197 095511 938399 895302 380006 166173 521832 876449 903266 > 32⁹⁷ [i]