Best Known (18, 49, s)-Nets in Base 32
(18, 49, 120)-Net over F32 — Constructive and digital
Digital (18, 49, 120)-net over F32, using
- t-expansion [i] based on digital (11, 49, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(18, 49, 161)-Net over F32 — Digital
Digital (18, 49, 161)-net over F32, using
- net from sequence [i] based on digital (18, 160)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 18 and N(F) ≥ 161, using
(18, 49, 192)-Net in Base 32 — Constructive
(18, 49, 192)-net in base 32, using
- t-expansion [i] based on (17, 49, 192)-net in base 32, using
- base change [i] based on digital (3, 35, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 35, 192)-net over F128, using
(18, 49, 215)-Net in Base 32
(18, 49, 215)-net in base 32, using
- base change [i] based on digital (4, 35, 215)-net over F128, using
- net from sequence [i] based on digital (4, 214)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 4 and N(F) ≥ 215, using
- net from sequence [i] based on digital (4, 214)-sequence over F128, using
(18, 49, 13572)-Net in Base 32 — Upper bound on s
There is no (18, 49, 13573)-net in base 32, because
- 1 times m-reduction [i] would yield (18, 48, 13573)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 768699 302078 728392 572666 463989 422074 078737 552850 263344 951009 628958 510336 > 3248 [i]