Best Known (254−104, 254, s)-Nets in Base 4
(254−104, 254, 138)-Net over F4 — Constructive and digital
Digital (150, 254, 138)-net over F4, using
- t-expansion [i] based on digital (149, 254, 138)-net over F4, using
- 5 times m-reduction [i] based on digital (149, 259, 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, 183, 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
- 5 times m-reduction [i] based on digital (149, 259, 138)-net over F4, using
(254−104, 254, 139)-Net in Base 4 — Constructive
(150, 254, 139)-net in base 4, using
- 2 times m-reduction [i] based on (150, 256, 139)-net in base 4, using
- (u, u+v)-construction [i] based on
- (24, 77, 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, 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
- (24, 77, 35)-net in base 4, using
- (u, u+v)-construction [i] based on
(254−104, 254, 335)-Net over F4 — Digital
Digital (150, 254, 335)-net over F4, using
(254−104, 254, 5840)-Net in Base 4 — Upper bound on s
There is no (150, 254, 5841)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 842 441153 537591 747353 853726 384656 054282 956818 927804 924983 224133 595201 393910 468881 620509 305418 257171 563350 008846 296050 201679 097390 553892 611938 036985 841360 > 4254 [i]