MinT - Best Known (68−53, 68, s)-Nets in Base 32

Best Known (68−53, 68, s)-Nets in Base 32

(68−53, 68, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 68, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 68, 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]

(68−53, 68, 158)-Net over F₃₂ — Digital

Digital (15, 68, 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]

(68−53, 68, 2560)-Net in Base 32 — Upper bound on s

There is no (15, 68, 2561)-net in base 32, because

1 times m-reduction [i] would yield (15, 67, 2561)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 70311 534927 257660 323992 483047 772611 324917 304604 797033 344415 633811 973228 755473 443509 385694 527043 077888 > 32⁶⁷ [i]