MinT - Best Known (8, 53, s)-Nets in Base 32

Best Known (8, 53, s)-Nets in Base 32

(8, 53, 98)-Net over F₃₂ — Constructive and digital

Digital (8, 53, 98)-net over F₃₂, using

t-expansion [i] based on digital (7, 53, 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]

(8, 53, 1043)-Net in Base 32 — Upper bound on s

There is no (8, 53, 1044)-net in base 32, because

1 times m-reduction [i] would yield (8, 52, 1044)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 872428 534106 890627 242116 327153 711156 871060 282223 536307 860206 999220 434456 996608 > 32⁵² [i]