Best Known (110−65, 110, s)-Nets in Base 32
(110−65, 110, 174)-Net over F32 — Constructive and digital
Digital (45, 110, 174)-net over F32, using
- 321 times duplication [i] based on digital (44, 109, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 37, 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, 72, 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, 37, 76)-net over F32, using
- (u, u+v)-construction [i] based on
(110−65, 110, 288)-Net in Base 32 — Constructive
(45, 110, 288)-net in base 32, using
- 322 times duplication [i] based on (43, 108, 288)-net in base 32, using
- t-expansion [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
- t-expansion [i] based on (40, 108, 288)-net in base 32, using
(110−65, 110, 325)-Net over F32 — Digital
Digital (45, 110, 325)-net over F32, using
- t-expansion [i] based on digital (44, 110, 325)-net over F32, using
- net from sequence [i] based on digital (44, 324)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 44 and N(F) ≥ 325, using
- net from sequence [i] based on digital (44, 324)-sequence over F32, using
(110−65, 110, 408)-Net in Base 32
(45, 110, 408)-net in base 32, using
- 322 times duplication [i] based on (43, 108, 408)-net in base 32, using
- base change [i] based on digital (25, 90, 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
- base change [i] based on digital (25, 90, 408)-net over F64, using
(110−65, 110, 55246)-Net in Base 32 — Upper bound on s
There is no (45, 110, 55247)-net in base 32, because
- 1 times m-reduction [i] would yield (45, 109, 55247)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 115 196337 030582 790414 436895 485105 500028 018238 749213 155614 790052 574750 565023 558807 296419 859198 008119 114207 315331 275868 427455 617845 152919 427400 075023 439619 785739 733138 > 32109 [i]