Best Known (69−46, 69, s)-Nets in Base 32
(69−46, 69, 120)-Net over F32 — Constructive and digital
Digital (23, 69, 120)-net over F32, using
- t-expansion [i] based on digital (11, 69, 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
(69−46, 69, 185)-Net over F32 — Digital
Digital (23, 69, 185)-net over F32, using
- t-expansion [i] based on digital (21, 69, 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
(69−46, 69, 192)-Net in Base 32 — Constructive
(23, 69, 192)-net in base 32, using
- 1 times m-reduction [i] based on (23, 70, 192)-net in base 32, using
- base change [i] based on digital (3, 50, 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, 50, 192)-net over F128, using
(69−46, 69, 225)-Net in Base 32
(23, 69, 225)-net in base 32, using
- 9 times m-reduction [i] based on (23, 78, 225)-net in base 32, using
- base change [i] based on digital (10, 65, 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, 65, 225)-net over F64, using
(69−46, 69, 9954)-Net in Base 32 — Upper bound on s
There is no (23, 69, 9955)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 71 704329 547505 677129 953643 106495 836556 117675 578851 671642 429817 530672 078496 208179 135900 321235 108853 563616 > 3269 [i]