MinT - Best Known (22−19, 22, s)-Nets in Base 32

Best Known (22−19, 22, s)-Nets in Base 32

(22−19, 22, 64)-Net over F₃₂ — Constructive and digital

Digital (3, 22, 64)-net over F₃₂, using

net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
  - a function field by SÃ©mirat [i]

(22−19, 22, 430)-Net in Base 32 — Upper bound on s

There is no (3, 22, 431)-net in base 32, because

1 times m-reduction [i] would yield (3, 21, 431)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 40 870501 397868 830805 868026 278038 > 32²¹ [i]