MinT - Best Known (16, 16+58, s)-Nets in Base 32

Best Known (16, 16+58, s)-Nets in Base 32

(16, 16+58, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 74, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 74, 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+58, 158)-Net over F₃₂ — Digital

Digital (16, 74, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 74, 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+58, 2594)-Net in Base 32 — Upper bound on s

There is no (16, 74, 2595)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2427 303425 990379 403799 738748 092191 260568 237172 305376 660905 375446 154820 023153 210694 769313 531263 621812 327455 861520 > 32⁷⁴ [i]