Best Known (52, 52+29, s)-Nets in Base 4
(52, 52+29, 130)-Net over F4 — Constructive and digital
Digital (52, 81, 130)-net over F4, using
- 11 times m-reduction [i] based on digital (52, 92, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 46, 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, 46, 65)-net over F16, using
(52, 52+29, 205)-Net over F4 — Digital
Digital (52, 81, 205)-net over F4, using
(52, 52+29, 5543)-Net in Base 4 — Upper bound on s
There is no (52, 81, 5544)-net in base 4, because
- 1 times m-reduction [i] would yield (52, 80, 5544)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 462308 347921 054709 768460 561963 264026 523145 856220 > 480 [i]