Best Known (155, 257, s)-Nets in Base 4
(155, 257, 138)-Net over F4 — Constructive and digital
Digital (155, 257, 138)-net over F4, using
- t-expansion [i] based on digital (149, 257, 138)-net over F4, using
- 2 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
- 2 times m-reduction [i] based on digital (149, 259, 138)-net over F4, using
(155, 257, 147)-Net in Base 4 — Constructive
(155, 257, 147)-net in base 4, using
- 2 times m-reduction [i] based on (155, 259, 147)-net in base 4, using
- (u, u+v)-construction [i] based on
- (30, 82, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-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
- (30, 82, 43)-net in base 4, using
- (u, u+v)-construction [i] based on
(155, 257, 375)-Net over F4 — Digital
Digital (155, 257, 375)-net over F4, using
(155, 257, 7113)-Net in Base 4 — Upper bound on s
There is no (155, 257, 7114)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 53756 976470 193434 164926 704110 947781 663263 429083 424656 264568 165173 116217 604883 939072 754991 899935 880415 474878 352852 249685 632796 681597 699015 058201 273297 773168 > 4257 [i]