Best Known (34, 34+44, s)-Nets in Base 32
(34, 34+44, 174)-Net over F32 — Constructive and digital
Digital (34, 78, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 27, 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, 51, 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, 27, 76)-net over F32, using
(34, 34+44, 288)-Net in Base 32 — Constructive
(34, 78, 288)-net in base 32, using
- t-expansion [i] based on (33, 78, 288)-net in base 32, using
- 6 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 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, 60, 288)-net over F128, using
- 6 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
(34, 34+44, 290)-Net over F32 — Digital
Digital (34, 78, 290)-net over F32, using
(34, 34+44, 342)-Net in Base 32
(34, 78, 342)-net in base 32, using
- 6 times m-reduction [i] based on (34, 84, 342)-net in base 32, using
- base change [i] based on digital (20, 70, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- base change [i] based on digital (20, 70, 342)-net over F64, using
(34, 34+44, 63365)-Net in Base 32 — Upper bound on s
There is no (34, 78, 63366)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2521 849265 646934 040633 445289 030457 057337 165771 903995 568981 613052 068609 973269 601019 483831 067995 787809 962906 457774 378048 > 3278 [i]