Best Known (180−78, 180, s)-Nets in Base 4
(180−78, 180, 130)-Net over F4 — Constructive and digital
Digital (102, 180, 130)-net over F4, using
- 12 times m-reduction [i] based on digital (102, 192, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 96, 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, 96, 65)-net over F16, using
(180−78, 180, 206)-Net over F4 — Digital
Digital (102, 180, 206)-net over F4, using
(180−78, 180, 3051)-Net in Base 4 — Upper bound on s
There is no (102, 180, 3052)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 359982 715987 698040 977645 694028 890420 821126 256592 446797 230626 129061 276298 392740 694967 633413 621524 564761 130970 > 4180 [i]