Best Known (47, 47+44, s)-Nets in Base 4
(47, 47+44, 60)-Net over F4 — Constructive and digital
Digital (47, 91, 60)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 32, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (15, 59, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (10, 32, 27)-net over F4, using
(47, 47+44, 65)-Net in Base 4 — Constructive
(47, 91, 65)-net in base 4, using
- 8 times m-reduction [i] based on (47, 99, 65)-net in base 4, using
- base change [i] based on digital (14, 66, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- base change [i] based on digital (14, 66, 65)-net over F8, using
(47, 47+44, 83)-Net over F4 — Digital
Digital (47, 91, 83)-net over F4, using
(47, 47+44, 915)-Net in Base 4 — Upper bound on s
There is no (47, 91, 916)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6 172977 850809 821089 024717 627443 082104 437084 946143 161504 > 491 [i]