MinT - Best Known (18, 18+92, s)-Nets in Base 32

Best Known (18, 18+92, s)-Nets in Base 32

(18, 18+92, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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+92, 161)-Net over F₃₂ — Digital

Digital (18, 110, 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+92, 2283)-Net in Base 32 — Upper bound on s

There is no (18, 110, 2284)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3718 062730 145064 214544 614595 309606 192231 413817 661927 937146 977605 306414 833143 851780 997313 285387 869188 692112 125205 261278 070261 359986 059632 610207 492246 664974 658304 646160 > 32¹¹⁰ [i]