Best Known (71−49, 71, s)-Nets in Base 32
(71−49, 71, 120)-Net over F32 — Constructive and digital
Digital (22, 71, 120)-net over F32, using
- t-expansion [i] based on digital (11, 71, 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
(71−49, 71, 177)-Net in Base 32 — Constructive
(22, 71, 177)-net in base 32, using
- 19 times m-reduction [i] based on (22, 90, 177)-net in base 32, using
- base change [i] based on digital (7, 75, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 75, 177)-net over F64, using
(71−49, 71, 185)-Net over F32 — Digital
Digital (22, 71, 185)-net over F32, using
- t-expansion [i] based on digital (21, 71, 185)-net over F32, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 21 and N(F) ≥ 185, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
(71−49, 71, 225)-Net in Base 32
(22, 71, 225)-net in base 32, using
- 1 times m-reduction [i] based on (22, 72, 225)-net in base 32, using
- base change [i] based on digital (10, 60, 225)-net over F64, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 10 and N(F) ≥ 225, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- base change [i] based on digital (10, 60, 225)-net over F64, using
(71−49, 71, 7750)-Net in Base 32 — Upper bound on s
There is no (22, 71, 7751)-net in base 32, because
- 1 times m-reduction [i] would yield (22, 70, 7751)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2296 399589 848883 681306 103670 221152 347180 526876 235228 508631 231383 694950 722476 510227 914830 043900 569739 017176 > 3270 [i]