MinT - Best Known (66−51, 66, s)-Nets in Base 32

Best Known (66−51, 66, s)-Nets in Base 32

(66−51, 66, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 66, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 66, 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]

(66−51, 66, 158)-Net over F₃₂ — Digital

Digital (15, 66, 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]

(66−51, 66, 2676)-Net in Base 32 — Upper bound on s

There is no (15, 66, 2677)-net in base 32, because

1 times m-reduction [i] would yield (15, 65, 2677)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 68 607007 528206 194556 769919 407107 060123 884011 872597 974526 417286 578824 006048 966818 871091 116087 655664 > 32⁶⁵ [i]