MinT - Best Known (7, 7+49, s)-Nets in Base 32

Best Known (7, 7+49, s)-Nets in Base 32

(7, 7+49, 98)-Net over F₃₂ — Constructive and digital

Digital (7, 56, 98)-net over F₃₂, using

net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
  - a function field by SÃ©mirat [i]

(7, 7+49, 877)-Net in Base 32 — Upper bound on s

There is no (7, 56, 878)-net in base 32, because

1 times m-reduction [i] would yield (7, 55, 878)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 61391 875809 416887 837185 081748 095255 655086 764099 625036 193355 626513 850863 318517 612674 > 32⁵⁵ [i]