MinT - Best Known (63−55, 63, s)-Nets in Base 32

Best Known (63−55, 63, s)-Nets in Base 32

(63−55, 63, 98)-Net over F₃₂ — Constructive and digital

Digital (8, 63, 98)-net over F₃₂, using

t-expansion [i] based on digital (7, 63, 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]

(63−55, 63, 993)-Net in Base 32 — Upper bound on s

There is no (8, 63, 994)-net in base 32, because

1 times m-reduction [i] would yield (8, 62, 994)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2095 232711 607103 822881 695442 126131 095347 970557 576353 711500 359824 050562 111750 828242 558475 582384 > 32⁶² [i]