MinT - Best Known (18, 18+81, s)-Nets in Base 32

Best Known (18, 18+81, s)-Nets in Base 32

(18, 18+81, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 99, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 99, 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]

(18, 18+81, 161)-Net over F₃₂ — Digital

Digital (18, 99, 161)-net over F₃₂, using

net from sequence [i] based on digital (18, 160)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 18 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(18, 18+81, 2456)-Net in Base 32 — Upper bound on s

There is no (18, 99, 2457)-net in base 32, because

1 times m-reduction [i] would yield (18, 98, 2457)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3199 949783 299161 108639 824694 111850 720798 268012 847135 441146 480446 190033 117900 398334 581913 125800 812900 702122 507983 143699 414463 804519 918921 920148 765620 > 32⁹⁸ [i]