Best Known (90−52, 90, s)-Nets in Base 32
(90−52, 90, 174)-Net over F32 — Constructive and digital
Digital (38, 90, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 31, 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, 59, 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, 31, 76)-net over F32, using
(90−52, 90, 288)-Net in Base 32 — Constructive
(38, 90, 288)-net in base 32, using
- t-expansion [i] based on (37, 90, 288)-net in base 32, using
- 8 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 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, 70, 288)-net over F128, using
- 8 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
(90−52, 90, 291)-Net over F32 — Digital
Digital (38, 90, 291)-net over F32, using
- net from sequence [i] based on digital (38, 290)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 38 and N(F) ≥ 291, using
(90−52, 90, 342)-Net in Base 32
(38, 90, 342)-net in base 32, using
- 18 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
- base change [i] based on digital (20, 90, 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, 90, 342)-net over F64, using
(90−52, 90, 55202)-Net in Base 32 — Upper bound on s
There is no (38, 90, 55203)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2907 653325 578669 418055 453904 877592 029171 823017 225442 259895 724334 889051 398248 197840 050186 262400 891673 585062 895394 079610 527527 073774 247260 > 3290 [i]