Best Known (149, 246, s)-Nets in Base 4
(149, 246, 138)-Net over F4 — Constructive and digital
Digital (149, 246, 138)-net over F4, using
- 13 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
(149, 246, 146)-Net in Base 4 — Constructive
(149, 246, 146)-net in base 4, using
- 1 times m-reduction [i] based on (149, 247, 146)-net in base 4, using
- (u, u+v)-construction [i] based on
- (27, 76, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- digital (73, 171, 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
- (27, 76, 42)-net in base 4, using
- (u, u+v)-construction [i] based on
(149, 246, 368)-Net over F4 — Digital
Digital (149, 246, 368)-net over F4, using
(149, 246, 7351)-Net in Base 4 — Upper bound on s
There is no (149, 246, 7352)-net in base 4, because
- 1 times m-reduction [i] would yield (149, 245, 7352)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3212 536649 096659 058314 455167 976021 377908 506076 614640 067042 630598 263106 979155 274536 194851 063248 429106 843816 488039 295333 043003 515080 249608 496498 903793 > 4245 [i]