Best Known (129, 129+74, s)-Nets in Base 4
(129, 129+74, 147)-Net over F4 — Constructive and digital
Digital (129, 203, 147)-net over F4, using
- 1 times m-reduction [i] based on digital (129, 204, 147)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 42, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (87, 162, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 81, 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, 81, 65)-net over F16, using
- digital (5, 42, 17)-net over F4, using
- (u, u+v)-construction [i] based on
(129, 129+74, 152)-Net in Base 4 — Constructive
(129, 203, 152)-net in base 4, using
- 3 times m-reduction [i] based on (129, 206, 152)-net in base 4, using
- trace code for nets [i] based on (26, 103, 76)-net in base 16, using
- 2 times m-reduction [i] based on (26, 105, 76)-net in base 16, using
- base change [i] based on digital (5, 84, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 84, 76)-net over F32, using
- 2 times m-reduction [i] based on (26, 105, 76)-net in base 16, using
- trace code for nets [i] based on (26, 103, 76)-net in base 16, using
(129, 129+74, 407)-Net over F4 — Digital
Digital (129, 203, 407)-net over F4, using
(129, 129+74, 9786)-Net in Base 4 — Upper bound on s
There is no (129, 203, 9787)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 165 368073 515096 690154 528229 785611 613201 482307 544692 980915 690597 337623 547567 898094 643798 757449 118502 681127 237912 498871 422460 > 4203 [i]