Best Known (145, 145+96, s)-Nets in Base 4
(145, 145+96, 138)-Net over F4 — Constructive and digital
Digital (145, 241, 138)-net over F4, using
- 6 times m-reduction [i] based on digital (145, 247, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 72, 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, 175, 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, 72, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(145, 145+96, 139)-Net in Base 4 — Constructive
(145, 241, 139)-net in base 4, using
- (u, u+v)-construction [i] based on
- (24, 72, 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, 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
- (24, 72, 35)-net in base 4, using
(145, 145+96, 350)-Net over F4 — Digital
Digital (145, 241, 350)-net over F4, using
(145, 145+96, 6544)-Net in Base 4 — Upper bound on s
There is no (145, 241, 6545)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12 494522 712079 516000 675156 749036 638265 317847 547209 673793 223268 107132 599981 273144 636785 296536 122416 178141 874403 156210 472638 359145 019492 618542 680908 > 4241 [i]