Best Known (91, 91+74, s)-Nets in Base 4
(91, 91+74, 130)-Net over F4 — Constructive and digital
Digital (91, 165, 130)-net over F4, using
- 5 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
(91, 91+74, 171)-Net over F4 — Digital
Digital (91, 165, 171)-net over F4, using
(91, 91+74, 2333)-Net in Base 4 — Upper bound on s
There is no (91, 165, 2334)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2192 621897 538702 609667 833235 064243 214443 856802 475802 473726 077090 032909 914423 382944 389388 526057 913960 > 4165 [i]