Best Known (125−56, 125, s)-Nets in Base 4
(125−56, 125, 130)-Net over F4 — Constructive and digital
Digital (69, 125, 130)-net over F4, using
- 1 times m-reduction [i] based on digital (69, 126, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 63, 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, 63, 65)-net over F16, using
(125−56, 125, 136)-Net over F4 — Digital
Digital (69, 125, 136)-net over F4, using
(125−56, 125, 1812)-Net in Base 4 — Upper bound on s
There is no (69, 125, 1813)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1827 536759 599912 651616 993946 996738 548459 617456 109879 468001 857393 022446 202400 > 4125 [i]