MinT - Best Known (54−43, 54, s)-Nets in Base 32

Best Known (54−43, 54, s)-Nets in Base 32

(54−43, 54, 120)-Net over F₃₂ — Constructive and digital

Digital (11, 54, 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]

(54−43, 54, 1750)-Net in Base 32 — Upper bound on s

There is no (11, 54, 1751)-net in base 32, because

1 times m-reduction [i] would yield (11, 53, 1751)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 59 515687 315804 139597 444862 859532 873433 459545 388735 397422 074364 000523 684319 129682 > 32⁵³ [i]