Best Known (16, 16+13, s)-Nets in Base 4
(16, 16+13, 48)-Net over F4 — Constructive and digital
Digital (16, 29, 48)-net over F4, using
- 1 times m-reduction [i] based on digital (16, 30, 48)-net over F4, using
- trace code for nets [i] based on digital (1, 15, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- trace code for nets [i] based on digital (1, 15, 24)-net over F16, using
(16, 16+13, 50)-Net over F4 — Digital
Digital (16, 29, 50)-net over F4, using
- 1 times m-reduction [i] based on digital (16, 30, 50)-net over F4, using
- trace code for nets [i] based on digital (1, 15, 25)-net over F16, using
- net from sequence [i] based on digital (1, 24)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 25, using
- net from sequence [i] based on digital (1, 24)-sequence over F16, using
- trace code for nets [i] based on digital (1, 15, 25)-net over F16, using
(16, 16+13, 639)-Net in Base 4 — Upper bound on s
There is no (16, 29, 640)-net in base 4, because
- 1 times m-reduction [i] would yield (16, 28, 640)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 72557 403726 165985 > 428 [i]