Best Known (61, 61+31, s)-Nets in Base 8
(61, 61+31, 368)-Net over F8 — Constructive and digital
Digital (61, 92, 368)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 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 (45, 76, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 38, 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, 38, 177)-net over F64, using
- digital (1, 16, 14)-net over F8, using
(61, 61+31, 520)-Net in Base 8 — Constructive
(61, 92, 520)-net in base 8, using
- base change [i] based on digital (38, 69, 520)-net over F16, using
- 1 times m-reduction [i] based on digital (38, 70, 520)-net over F16, using
- trace code for nets [i] based on digital (3, 35, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 35, 260)-net over F256, using
- 1 times m-reduction [i] based on digital (38, 70, 520)-net over F16, using
(61, 61+31, 1027)-Net over F8 — Digital
Digital (61, 92, 1027)-net over F8, using
(61, 61+31, 276312)-Net in Base 8 — Upper bound on s
There is no (61, 92, 276313)-net in base 8, because
- 1 times m-reduction [i] would yield (61, 91, 276313)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 15177 712050 309748 020358 606782 213601 715387 906938 002335 047002 477562 859905 705922 661776 > 891 [i]