Best Known (152, 260, s)-Nets in Base 4
(152, 260, 138)-Net over F4 — Constructive and digital
Digital (152, 260, 138)-net over F4, using
- t-expansion [i] based on digital (149, 260, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 76, 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, 184, 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, 76, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(152, 260, 139)-Net in Base 4 — Constructive
(152, 260, 139)-net in base 4, using
- t-expansion [i] based on (151, 260, 139)-net in base 4, using
- (u, u+v)-construction [i] based on
- (24, 78, 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, 182, 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, 78, 35)-net in base 4, using
- (u, u+v)-construction [i] based on
(152, 260, 327)-Net over F4 — Digital
Digital (152, 260, 327)-net over F4, using
(152, 260, 5492)-Net in Base 4 — Upper bound on s
There is no (152, 260, 5493)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 464135 258428 114755 105176 993268 047330 067958 474663 149266 779950 733176 539303 258904 325607 945534 682732 293331 618356 586477 720777 323506 325257 653504 518715 821981 682736 > 4260 [i]