Best Known (127−56, 127, s)-Nets in Base 4
(127−56, 127, 130)-Net over F4 — Constructive and digital
Digital (71, 127, 130)-net over F4, using
- 3 times m-reduction [i] based on digital (71, 130, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 65, 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, 65, 65)-net over F16, using
(127−56, 127, 145)-Net over F4 — Digital
Digital (71, 127, 145)-net over F4, using
(127−56, 127, 2003)-Net in Base 4 — Upper bound on s
There is no (71, 127, 2004)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 29212 516508 655795 474353 678846 713688 623954 569850 405572 052903 120905 081741 117808 > 4127 [i]