Best Known (239−92, 239, s)-Nets in Base 4
(239−92, 239, 138)-Net over F4 — Constructive and digital
Digital (147, 239, 138)-net over F4, using
- 14 times m-reduction [i] based on digital (147, 253, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 74, 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, 179, 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, 74, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(239−92, 239, 146)-Net in Base 4 — Constructive
(147, 239, 146)-net in base 4, using
- 2 times m-reduction [i] based on (147, 241, 146)-net in base 4, using
- (u, u+v)-construction [i] based on
- (27, 74, 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, 167, 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, 74, 42)-net in base 4, using
- (u, u+v)-construction [i] based on
(239−92, 239, 389)-Net over F4 — Digital
Digital (147, 239, 389)-net over F4, using
(239−92, 239, 8019)-Net in Base 4 — Upper bound on s
There is no (147, 239, 8020)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 781413 109670 725773 181612 592983 179707 597004 582352 734098 167166 368667 323726 791802 999053 963203 946457 394566 876037 349846 273293 692849 253378 218687 096936 > 4239 [i]