MinT - Best Known (69−57, 69, s)-Nets in Base 32

Best Known (69−57, 69, s)-Nets in Base 32

(69−57, 69, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 69, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 69, 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]

(69−57, 69, 129)-Net over F₃₂ — Digital

Digital (12, 69, 129)-net over F₃₂, using

net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(69−57, 69, 1633)-Net in Base 32 — Upper bound on s

There is no (12, 69, 1634)-net in base 32, because

1 times m-reduction [i] would yield (12, 68, 1634)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 246784 088955 436173 482520 951746 109450 147309 975222 824461 323873 844471 896588 237443 719202 070981 327234 159976 > 32⁶⁸ [i]