Best Known (67, 102, s)-Nets in Base 8
(67, 102, 368)-Net over F8 — Constructive and digital
Digital (67, 102, 368)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- digital (49, 84, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 42, 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, 42, 177)-net over F64, using
- digital (1, 18, 14)-net over F8, using
(67, 102, 520)-Net in Base 8 — Constructive
(67, 102, 520)-net in base 8, using
- trace code for nets [i] based on (16, 51, 260)-net in base 64, using
- 1 times m-reduction [i] based on (16, 52, 260)-net in base 64, using
- base change [i] based on digital (3, 39, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 39, 260)-net over F256, using
- 1 times m-reduction [i] based on (16, 52, 260)-net in base 64, using
(67, 102, 1007)-Net over F8 — Digital
Digital (67, 102, 1007)-net over F8, using
(67, 102, 237818)-Net in Base 8 — Upper bound on s
There is no (67, 102, 237819)-net in base 8, because
- 1 times m-reduction [i] would yield (67, 101, 237819)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 16 297208 861771 650460 326439 382330 716881 022237 532091 772937 411005 451037 692825 353700 175590 918710 > 8101 [i]