Best Known (147, 243, s)-Nets in Base 4
(147, 243, 138)-Net over F4 — Constructive and digital
Digital (147, 243, 138)-net over F4, using
- 10 times m-reduction [i] based on digital (147, 253, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 74, 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, 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
- digital (21, 74, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(147, 243, 140)-Net in Base 4 — Constructive
(147, 243, 140)-net in base 4, using
- (u, u+v)-construction [i] based on
- (26, 74, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-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 3 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]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-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
- (26, 74, 36)-net in base 4, using
(147, 243, 362)-Net over F4 — Digital
Digital (147, 243, 362)-net over F4, using
(147, 243, 6936)-Net in Base 4 — Upper bound on s
There is no (147, 243, 6937)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 200 567760 796141 708823 057286 529133 329007 124596 457765 258077 789431 216467 364357 695811 045704 979156 291431 044285 101233 523752 396326 179264 882947 039438 369160 > 4243 [i]