Best Known (87−34, 87, s)-Nets in Base 4
(87−34, 87, 130)-Net over F4 — Constructive and digital
Digital (53, 87, 130)-net over F4, using
- 7 times m-reduction [i] based on digital (53, 94, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 47, 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, 47, 65)-net over F16, using
(87−34, 87, 159)-Net over F4 — Digital
Digital (53, 87, 159)-net over F4, using
(87−34, 87, 2870)-Net in Base 4 — Upper bound on s
There is no (53, 87, 2871)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 24074 346511 805846 708532 071500 581060 215675 209343 209906 > 487 [i]