Best Known (99, 144, s)-Nets in Base 8
(99, 144, 419)-Net over F8 — Constructive and digital
Digital (99, 144, 419)-net over F8, using
- t-expansion [i] based on digital (98, 144, 419)-net over F8, using
- 1 times m-reduction [i] based on digital (98, 145, 419)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 37, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (61, 108, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 54, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 54, 177)-net over F64, using
- digital (14, 37, 65)-net over F8, using
- (u, u+v)-construction [i] based on
- 1 times m-reduction [i] based on digital (98, 145, 419)-net over F8, using
(99, 144, 576)-Net in Base 8 — Constructive
(99, 144, 576)-net in base 8, using
- t-expansion [i] based on (97, 144, 576)-net in base 8, using
- 10 times m-reduction [i] based on (97, 154, 576)-net in base 8, using
- trace code for nets [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
- trace code for nets [i] based on (20, 77, 288)-net in base 64, using
- 10 times m-reduction [i] based on (97, 154, 576)-net in base 8, using
(99, 144, 2247)-Net over F8 — Digital
Digital (99, 144, 2247)-net over F8, using
(99, 144, 959033)-Net in Base 8 — Upper bound on s
There is no (99, 144, 959034)-net in base 8, because
- 1 times m-reduction [i] would yield (99, 143, 959034)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1386 354502 164882 688994 752967 568873 354307 926785 630515 636932 981703 484248 251313 843304 870392 665762 590577 142509 185781 028076 317768 864244 > 8143 [i]