MinT - Best Known (18, 18+69, s)-Nets in Base 32

Best Known (18, 18+69, s)-Nets in Base 32

(18, 18+69, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 87, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 87, 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+69, 161)-Net over F₃₂ — Digital

Digital (18, 87, 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+69, 2783)-Net in Base 32 — Upper bound on s

There is no (18, 87, 2784)-net in base 32, because

1 times m-reduction [i] would yield (18, 86, 2784)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2804 134380 403380 211084 657071 619664 699082 878914 406177 654153 778744 808963 661617 274230 564208 677844 220022 607127 495363 604865 824519 143678 > 32⁸⁶ [i]