MinT - Best Known (15, 15+85, s)-Nets in Base 32

Best Known (15, 15+85, s)-Nets in Base 32

(15, 15+85, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 100, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 100, 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+85, 158)-Net over F₃₂ — Digital

Digital (15, 100, 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+85, 1858)-Net in Base 32 — Upper bound on s

There is no (15, 100, 1859)-net in base 32, because

1 times m-reduction [i] would yield (15, 99, 1859)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 102780 121192 330232 066869 243551 021047 966018 656217 118207 195815 559739 195467 604241 543282 711293 223454 646943 663792 383865 399648 260603 303401 531086 965255 304840 > 32⁹⁹ [i]