Best Known (163−72, 163, s)-Nets in Base 4
(163−72, 163, 130)-Net over F4 — Constructive and digital
Digital (91, 163, 130)-net over F4, using
- 7 times m-reduction [i] based on digital (91, 170, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 85, 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, 85, 65)-net over F16, using
(163−72, 163, 178)-Net over F4 — Digital
Digital (91, 163, 178)-net over F4, using
(163−72, 163, 2503)-Net in Base 4 — Upper bound on s
There is no (91, 163, 2504)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 137 712777 127879 051870 488917 633269 877548 597971 425827 293409 848763 352419 794856 940846 040561 175351 204702 > 4163 [i]