Best Known (133, 133+70, s)-Nets in Base 4
(133, 133+70, 163)-Net over F4 — Constructive and digital
Digital (133, 203, 163)-net over F4, using
- 1 times m-reduction [i] based on digital (133, 204, 163)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 50, 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 (83, 154, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 77, 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, 77, 65)-net over F16, using
- digital (15, 50, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(133, 133+70, 208)-Net in Base 4 — Constructive
(133, 203, 208)-net in base 4, using
- 3 times m-reduction [i] based on (133, 206, 208)-net in base 4, using
- trace code for nets [i] based on (30, 103, 104)-net in base 16, using
- 2 times m-reduction [i] based on (30, 105, 104)-net in base 16, using
- base change [i] based on digital (9, 84, 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, 84, 104)-net over F32, using
- 2 times m-reduction [i] based on (30, 105, 104)-net in base 16, using
- trace code for nets [i] based on (30, 103, 104)-net in base 16, using
(133, 133+70, 493)-Net over F4 — Digital
Digital (133, 203, 493)-net over F4, using
(133, 133+70, 14362)-Net in Base 4 — Upper bound on s
There is no (133, 203, 14363)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 165 529858 782394 455161 573638 692940 406354 533509 715094 495350 397420 119206 593588 911840 333507 642422 081281 231604 770352 812599 061248 > 4203 [i]