Best Known (147, 245, s)-Nets in Base 4
(147, 245, 138)-Net over F4 — Constructive and digital
Digital (147, 245, 138)-net over F4, using
- 8 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
(147, 245, 139)-Net in Base 4 — Constructive
(147, 245, 139)-net in base 4, using
- 2 times m-reduction [i] based on (147, 247, 139)-net in base 4, using
- (u, u+v)-construction [i] based on
- (24, 74, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-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 2 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]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- digital (73, 173, 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
- (24, 74, 35)-net in base 4, using
- (u, u+v)-construction [i] based on
(147, 245, 350)-Net over F4 — Digital
Digital (147, 245, 350)-net over F4, using
(147, 245, 6483)-Net in Base 4 — Upper bound on s
There is no (147, 245, 6484)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3212 160850 826709 104723 952583 183807 708818 986779 649365 295550 810855 041478 731565 332248 745713 384585 401489 588331 336069 936127 354273 233097 323305 052114 933666 > 4245 [i]