Best Known (42, 42+60, s)-Nets in Base 32
(42, 42+60, 174)-Net over F32 — Constructive and digital
Digital (42, 102, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 35, 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, 67, 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, 35, 76)-net over F32, using
(42, 42+60, 288)-Net in Base 32 — Constructive
(42, 102, 288)-net in base 32, using
- t-expansion [i] based on (40, 102, 288)-net in base 32, using
- 6 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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, 78, 288)-net over F128, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 6 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(42, 42+60, 308)-Net over F32 — Digital
Digital (42, 102, 308)-net over F32, using
- t-expansion [i] based on digital (41, 102, 308)-net over F32, using
- net from sequence [i] based on digital (41, 307)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 41 and N(F) ≥ 308, using
- net from sequence [i] based on digital (41, 307)-sequence over F32, using
(42, 42+60, 408)-Net in Base 32
(42, 102, 408)-net in base 32, using
- base change [i] based on digital (25, 85, 408)-net over F64, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 25 and N(F) ≥ 408, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
(42, 42+60, 50910)-Net in Base 32 — Upper bound on s
There is no (42, 102, 50911)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3353 490777 238062 587392 668757 411615 922722 446358 472242 766164 040114 619871 575107 503149 984385 394500 083790 602166 131880 465490 149310 418874 282052 933714 813532 713037 > 32102 [i]