MinT - Best Known (16, 16+56, s)-Nets in Base 32

Best Known (16, 16+56, s)-Nets in Base 32

(16, 16+56, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 72, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 72, 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]

(16, 16+56, 158)-Net over F₃₂ — Digital

Digital (16, 72, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 72, 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]

(16, 16+56, 2689)-Net in Base 32 — Upper bound on s

There is no (16, 72, 2690)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 354571 983801 812485 056734 219567 967195 264568 097639 293147 247114 600745 675073 571548 529792 401817 681874 424075 146784 > 32⁷² [i]