Best Known (52, 52+40, s)-Nets in Base 4
(52, 52+40, 130)-Net over F4 — Constructive and digital
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
(52, 52+40, 1611)-Net in Base 4 — Upper bound on s
There is no (52, 92, 1612)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 24 544159 722572 123936 845080 409624 662565 066089 905032 511896 > 492 [i]