MinT - Best Known (72−59, 72, s)-Nets in Base 32

Best Known (72−59, 72, s)-Nets in Base 32

(72−59, 72, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 72, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 72, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(72−59, 72, 129)-Net over F₃₂ — Digital

Digital (13, 72, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 72, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(72−59, 72, 1808)-Net in Base 32 — Upper bound on s

There is no (13, 72, 1809)-net in base 32, because

1 times m-reduction [i] would yield (13, 71, 1809)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 74480 327487 793859 815992 325568 113597 498327 181965 523688 320030 102488 347803 214774 076356 575164 443932 293169 147648 > 32⁷¹ [i]