Best Known (195−73, 195, s)-Nets in Base 4
(195−73, 195, 139)-Net over F4 — Constructive and digital
Digital (122, 195, 139)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 37, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (85, 158, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 79, 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, 79, 65)-net over F16, using
- digital (1, 37, 9)-net over F4, using
(195−73, 195, 358)-Net over F4 — Digital
Digital (122, 195, 358)-net over F4, using
(195−73, 195, 8327)-Net in Base 4 — Upper bound on s
There is no (122, 195, 8328)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 194, 8328)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 631 691856 740200 000316 101770 358459 863084 633153 786299 310315 609546 041547 632325 995493 420803 914154 452087 503178 009906 088500 > 4194 [i]