Best Known (125, 191, s)-Nets in Base 4
(125, 191, 160)-Net over F4 — Constructive and digital
Digital (125, 191, 160)-net over F4, using
- 1 times m-reduction [i] based on digital (125, 192, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 46, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- digital (79, 146, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 73, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 73, 65)-net over F16, using
- digital (13, 46, 30)-net over F4, using
- (u, u+v)-construction [i] based on
(125, 191, 208)-Net in Base 4 — Constructive
(125, 191, 208)-net in base 4, using
- 41 times duplication [i] based on (124, 190, 208)-net in base 4, using
- t-expansion [i] based on (123, 190, 208)-net in base 4, using
- trace code for nets [i] based on (28, 95, 104)-net in base 16, using
- base change [i] based on digital (9, 76, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 76, 104)-net over F32, using
- trace code for nets [i] based on (28, 95, 104)-net in base 16, using
- t-expansion [i] based on (123, 190, 208)-net in base 4, using
(125, 191, 464)-Net over F4 — Digital
Digital (125, 191, 464)-net over F4, using
(125, 191, 13366)-Net in Base 4 — Upper bound on s
There is no (125, 191, 13367)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9 870362 346703 552727 555716 173880 111229 456785 322662 347631 019034 770885 020692 956232 173640 539688 339742 471783 275378 764074 > 4191 [i]