Best Known (47, 94, s)-Nets in Base 4
(47, 94, 57)-Net over F4 — Constructive and digital
Digital (47, 94, 57)-net over F4, using
- 1 times m-reduction [i] based on digital (47, 95, 57)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 34, 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 (13, 61, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- digital (10, 34, 27)-net over F4, using
- (u, u+v)-construction [i] based on
(47, 94, 65)-Net in Base 4 — Constructive
(47, 94, 65)-net in base 4, using
- 5 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, 94, 81)-Net over F4 — Digital
Digital (47, 94, 81)-net over F4, using
- t-expansion [i] based on digital (46, 94, 81)-net over F4, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 46 and N(F) ≥ 81, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
(47, 94, 836)-Net in Base 4 — Upper bound on s
There is no (47, 94, 837)-net in base 4, because
- 1 times m-reduction [i] would yield (47, 93, 837)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 100 574149 757585 186973 955184 543627 793582 630612 511898 156608 > 493 [i]