Best Known (146, 240, s)-Nets in Base 4
(146, 240, 138)-Net over F4 — Constructive and digital
Digital (146, 240, 138)-net over F4, using
- 10 times m-reduction [i] based on digital (146, 250, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 73, 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, 177, 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, 73, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(146, 240, 140)-Net in Base 4 — Constructive
(146, 240, 140)-net in base 4, using
- (u, u+v)-construction [i] based on
- (26, 73, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-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
- (26, 73, 36)-net in base 4, using
(146, 240, 368)-Net over F4 — Digital
Digital (146, 240, 368)-net over F4, using
(146, 240, 7227)-Net in Base 4 — Upper bound on s
There is no (146, 240, 7228)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 122964 154028 366197 291345 275496 891103 135712 889743 770856 678551 776424 270548 891846 643139 626123 821903 670169 539734 507925 692190 983150 194401 876801 650228 > 4240 [i]