Best Known (107, 107+54, s)-Nets in Base 4
(107, 107+54, 160)-Net over F4 — Constructive and digital
Digital (107, 161, 160)-net over F4, using
- 1 times m-reduction [i] based on digital (107, 162, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 40, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 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) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- digital (67, 122, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F16, using
- digital (13, 40, 30)-net over F4, using
- (u, u+v)-construction [i] based on
(107, 107+54, 208)-Net in Base 4 — Constructive
(107, 161, 208)-net in base 4, using
- 41 times duplication [i] based on (106, 160, 208)-net in base 4, using
- t-expansion [i] based on (105, 160, 208)-net in base 4, using
- trace code for nets [i] based on (25, 80, 104)-net in base 16, using
- base change [i] based on digital (9, 64, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 64, 104)-net over F32, using
- trace code for nets [i] based on (25, 80, 104)-net in base 16, using
- t-expansion [i] based on (105, 160, 208)-net in base 4, using
(107, 107+54, 446)-Net over F4 — Digital
Digital (107, 161, 446)-net over F4, using
(107, 107+54, 14147)-Net in Base 4 — Upper bound on s
There is no (107, 161, 14148)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 555909 265832 001703 753363 061378 791837 608694 162228 996719 222625 016232 034826 460118 362337 333731 177272 > 4161 [i]