MinT - Best Known (57−49, 57, s)-Nets in Base 32

Best Known (57−49, 57, s)-Nets in Base 32

(57−49, 57, 98)-Net over F₃₂ — Constructive and digital

Digital (8, 57, 98)-net over F₃₂, using

t-expansion [i] based on digital (7, 57, 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]

(57−49, 57, 1015)-Net in Base 32 — Upper bound on s

There is no (8, 57, 1016)-net in base 32, because

1 times m-reduction [i] would yield (8, 56, 1016)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 951027 320380 864704 598564 534973 238222 392618 801628 275123 259071 806948 904502 979069 686172 > 32⁵⁶ [i]