Best Known (130, 197, s)-Nets in Base 4
(130, 197, 163)-Net over F4 — Constructive and digital
Digital (130, 197, 163)-net over F4, using
- 2 times m-reduction [i] based on digital (130, 199, 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 (81, 150, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 75, 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, 75, 65)-net over F16, using
- digital (15, 49, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(130, 197, 240)-Net in Base 4 — Constructive
(130, 197, 240)-net in base 4, using
- 1 times m-reduction [i] based on (130, 198, 240)-net in base 4, using
- trace code for nets [i] based on (31, 99, 120)-net in base 16, using
- 1 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
- 1 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
- trace code for nets [i] based on (31, 99, 120)-net in base 16, using
(130, 197, 504)-Net over F4 — Digital
Digital (130, 197, 504)-net over F4, using
(130, 197, 16496)-Net in Base 4 — Upper bound on s
There is no (130, 197, 16497)-net in base 4, because
- 1 times m-reduction [i] would yield (130, 196, 16497)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10094 903755 074559 617352 784327 557441 686497 969326 959223 862653 783535 238338 417025 724802 076743 495136 805719 783387 964010 586388 > 4196 [i]