Best Known (252−103, 252, s)-Nets in Base 4
(252−103, 252, 138)-Net over F4 — Constructive and digital
Digital (149, 252, 138)-net over F4, using
- 7 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
(252−103, 252, 139)-Net in Base 4 — Constructive
(149, 252, 139)-net in base 4, using
- 1 times m-reduction [i] based on (149, 253, 139)-net in base 4, using
- (u, u+v)-construction [i] based on
- (24, 76, 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, 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
- (24, 76, 35)-net in base 4, using
- (u, u+v)-construction [i] based on
(252−103, 252, 335)-Net over F4 — Digital
Digital (149, 252, 335)-net over F4, using
(252−103, 252, 6036)-Net in Base 4 — Upper bound on s
There is no (149, 252, 6037)-net in base 4, because
- 1 times m-reduction [i] would yield (149, 251, 6037)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13 109169 666132 081064 969188 606992 807396 018282 708148 860208 973769 215818 116913 868171 309983 752923 154205 130276 639625 295720 488127 021415 875817 843416 768334 451440 > 4251 [i]