Best Known (73−41, 73, s)-Nets in Base 32
(73−41, 73, 174)-Net over F32 — Constructive and digital
Digital (32, 73, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 25, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (7, 48, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (5, 25, 76)-net over F32, using
(73−41, 73, 283)-Net over F32 — Digital
Digital (32, 73, 283)-net over F32, using
(73−41, 73, 288)-Net in Base 32 — Constructive
(32, 73, 288)-net in base 32, using
- t-expansion [i] based on (31, 73, 288)-net in base 32, using
- 4 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
- base change [i] based on digital (9, 55, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 55, 288)-net over F128, using
- 4 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
(73−41, 73, 321)-Net in Base 32
(32, 73, 321)-net in base 32, using
- 7 times m-reduction [i] based on (32, 80, 321)-net in base 32, using
- base change [i] based on digital (2, 50, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 50, 321)-net over F256, using
(73−41, 73, 70213)-Net in Base 32 — Upper bound on s
There is no (32, 73, 70214)-net in base 32, because
- 1 times m-reduction [i] would yield (32, 72, 70214)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 348758 929124 082419 727338 912335 970411 049360 858059 944742 658249 086054 446676 617771 038670 151880 948774 245673 016604 > 3272 [i]