Best Known (93, 93+74, s)-Nets in Base 4
(93, 93+74, 130)-Net over F4 — Constructive and digital
Digital (93, 167, 130)-net over F4, using
- 7 times m-reduction [i] based on digital (93, 174, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 87, 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, 87, 65)-net over F16, using
(93, 93+74, 180)-Net over F4 — Digital
Digital (93, 167, 180)-net over F4, using
(93, 93+74, 2517)-Net in Base 4 — Upper bound on s
There is no (93, 167, 2518)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 35104 454854 923255 880791 695986 107312 441938 674338 510122 405787 250716 153198 588765 891736 984716 064278 102250 > 4167 [i]