Best Known (156, 156+104, s)-Nets in Base 4
(156, 156+104, 138)-Net over F4 — Constructive and digital
Digital (156, 260, 138)-net over F4, using
- t-expansion [i] based on digital (149, 260, 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, 184, 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
(156, 156+104, 147)-Net in Base 4 — Constructive
(156, 260, 147)-net in base 4, using
- t-expansion [i] based on (155, 260, 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, 178, 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
(156, 156+104, 369)-Net over F4 — Digital
Digital (156, 260, 369)-net over F4, using
(156, 156+104, 6860)-Net in Base 4 — Upper bound on s
There is no (156, 260, 6861)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 435744 700648 609157 742241 963674 683606 275853 123630 357670 773759 739097 600034 779384 110215 972193 417275 329456 679206 936645 274652 410920 222236 490733 096616 372429 386356 > 4260 [i]