Best Known (48, 48+45, s)-Nets in Base 4
(48, 48+45, 60)-Net over F4 — Constructive and digital
Digital (48, 93, 60)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 35, 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 (13, 58, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4 (see above)
- digital (13, 35, 30)-net over F4, using
(48, 48+45, 65)-Net in Base 4 — Constructive
(48, 93, 65)-net in base 4, using
- 9 times m-reduction [i] based on (48, 102, 65)-net in base 4, using
- base change [i] based on digital (14, 68, 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, 68, 65)-net over F8, using
(48, 48+45, 84)-Net over F4 — Digital
Digital (48, 93, 84)-net over F4, using
(48, 48+45, 976)-Net in Base 4 — Upper bound on s
There is no (48, 93, 977)-net in base 4, because
- 1 times m-reduction [i] would yield (48, 92, 977)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 24 844684 513831 255587 778181 867858 677669 310928 033910 000480 > 492 [i]