MinT - Best Known (74−61, 74, s)-Nets in Base 32

Best Known (74−61, 74, s)-Nets in Base 32

(74−61, 74, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 74, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 74, 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]

(74−61, 74, 129)-Net over F₃₂ — Digital

Digital (13, 74, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 74, 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]

(74−61, 74, 1770)-Net in Base 32 — Upper bound on s

There is no (13, 74, 1771)-net in base 32, because

1 times m-reduction [i] would yield (13, 73, 1771)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 75 306829 921688 681703 628772 719053 247170 728438 572417 848264 713482 186897 923893 361004 492136 537930 019104 361450 018952 > 32⁷³ [i]