Best Known (129, 129+66, s)-Nets in Base 4
(129, 129+66, 163)-Net over F4 — Constructive and digital
Digital (129, 195, 163)-net over F4, using
- 2 times m-reduction [i] based on digital (129, 197, 163)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 49, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (80, 148, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 74, 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, 74, 65)-net over F16, using
- digital (15, 49, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(129, 129+66, 240)-Net in Base 4 — Constructive
(129, 195, 240)-net in base 4, using
- 1 times m-reduction [i] based on (129, 196, 240)-net in base 4, using
- trace code for nets [i] based on (31, 98, 120)-net in base 16, using
- 2 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
- base change [i] based on digital (11, 80, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 80, 120)-net over F32, using
- 2 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
- trace code for nets [i] based on (31, 98, 120)-net in base 16, using
(129, 129+66, 509)-Net over F4 — Digital
Digital (129, 195, 509)-net over F4, using
(129, 129+66, 15816)-Net in Base 4 — Upper bound on s
There is no (129, 195, 15817)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2522 546966 376439 113177 155028 390688 754155 165382 599318 953757 300147 313452 659462 622391 468140 924848 362697 016484 570798 011960 > 4195 [i]