Best Known (43, 43+41, s)-Nets in Base 4
(43, 43+41, 57)-Net over F4 — Constructive and digital
Digital (43, 84, 57)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 30, 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, 54, 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, 30, 27)-net over F4, using
(43, 43+41, 65)-Net in Base 4 — Constructive
(43, 84, 65)-net in base 4, using
- 3 times m-reduction [i] based on (43, 87, 65)-net in base 4, using
- base change [i] based on digital (14, 58, 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, 58, 65)-net over F8, using
(43, 43+41, 76)-Net over F4 — Digital
Digital (43, 84, 76)-net over F4, using
(43, 43+41, 856)-Net in Base 4 — Upper bound on s
There is no (43, 84, 857)-net in base 4, because
- 1 times m-reduction [i] would yield (43, 83, 857)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 94 864258 188734 333334 346762 103683 196877 081351 667594 > 483 [i]