Best Known (148, 148+94, s)-Nets in Base 4
(148, 148+94, 138)-Net over F4 — Constructive and digital
Digital (148, 242, 138)-net over F4, using
- 14 times m-reduction [i] based on digital (148, 256, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 75, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- digital (73, 181, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- digital (21, 75, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(148, 148+94, 146)-Net in Base 4 — Constructive
(148, 242, 146)-net in base 4, using
- 2 times m-reduction [i] based on (148, 244, 146)-net in base 4, using
- (u, u+v)-construction [i] based on
- (27, 75, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- digital (73, 169, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- (27, 75, 42)-net in base 4, using
- (u, u+v)-construction [i] based on
(148, 148+94, 381)-Net over F4 — Digital
Digital (148, 242, 381)-net over F4, using
(148, 148+94, 7669)-Net in Base 4 — Upper bound on s
There is no (148, 242, 7670)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 50 102667 344121 998356 644252 472543 292689 615928 470875 530670 122388 773757 992935 982455 825634 429056 471195 430368 145207 636777 555027 625370 318083 320675 632648 > 4242 [i]