Best Known (82, 117, s)-Nets in Base 8
(82, 117, 419)-Net over F8 — Constructive and digital
Digital (82, 117, 419)-net over F8, using
- 1 times m-reduction [i] based on digital (82, 118, 419)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 32, 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 (50, 86, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 43, 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, 43, 177)-net over F64, using
- digital (14, 32, 65)-net over F8, using
- (u, u+v)-construction [i] based on
(82, 117, 576)-Net in Base 8 — Constructive
(82, 117, 576)-net in base 8, using
- t-expansion [i] based on (81, 117, 576)-net in base 8, using
- 9 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 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, 54, 288)-net over F128, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
- 9 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
(82, 117, 2495)-Net over F8 — Digital
Digital (82, 117, 2495)-net over F8, using
(82, 117, 1489721)-Net in Base 8 — Upper bound on s
There is no (82, 117, 1489722)-net in base 8, because
- 1 times m-reduction [i] would yield (82, 116, 1489722)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 573 375038 631848 896492 157295 659445 683035 809108 585741 119810 904803 806697 537872 208340 613766 225600 127058 915631 > 8116 [i]