Best Known (78, 78+43, s)-Nets in Base 8
(78, 78+43, 363)-Net over F8 — Constructive and digital
Digital (78, 121, 363)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 21, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (57, 100, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 50, 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, 50, 177)-net over F64, using
- digital (0, 21, 9)-net over F8, using
(78, 78+43, 518)-Net in Base 8 — Constructive
(78, 121, 518)-net in base 8, using
- 81 times duplication [i] based on (77, 120, 518)-net in base 8, using
- base change [i] based on digital (47, 90, 518)-net over F16, using
- trace code for nets [i] based on digital (2, 45, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 45, 259)-net over F256, using
- base change [i] based on digital (47, 90, 518)-net over F16, using
(78, 78+43, 964)-Net over F8 — Digital
Digital (78, 121, 964)-net over F8, using
(78, 78+43, 179422)-Net in Base 8 — Upper bound on s
There is no (78, 121, 179423)-net in base 8, because
- 1 times m-reduction [i] would yield (78, 120, 179423)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 2 348637 983907 195629 255721 663250 203403 687344 707044 109928 863166 808641 651828 817798 223917 643190 383570 708711 850082 > 8120 [i]