MinT - Best Known (15, 15+83, s)-Nets in Base 32

Best Known (15, 15+83, s)-Nets in Base 32

(15, 15+83, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 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]

(15, 15+83, 158)-Net over F₃₂ — Digital

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]

(15, 15+83, 1873)-Net in Base 32 — Upper bound on s

There is no (15, 98, 1874)-net in base 32, because

1 times m-reduction [i] would yield (15, 97, 1874)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 101 374276 252095 184711 458903 943792 949059 998074 306970 768682 421759 635901 766082 085151 435225 641662 366248 025471 474106 517233 484712 819741 310412 142273 465980 > 32⁹⁷ [i]