Best Known (90, 138, s)-Nets in Base 4
(90, 138, 147)-Net over F4 — Constructive and digital
Digital (90, 138, 147)-net over F4, using
- 1 times m-reduction [i] based on digital (90, 139, 147)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 29, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (61, 110, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 55, 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, 55, 65)-net over F16, using
- digital (5, 29, 17)-net over F4, using
- (u, u+v)-construction [i] based on
(90, 138, 196)-Net in Base 4 — Constructive
(90, 138, 196)-net in base 4, using
- trace code for nets [i] based on (21, 69, 98)-net in base 16, using
- 1 times m-reduction [i] based on (21, 70, 98)-net in base 16, using
- base change [i] based on digital (7, 56, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 56, 98)-net over F32, using
- 1 times m-reduction [i] based on (21, 70, 98)-net in base 16, using
(90, 138, 344)-Net over F4 — Digital
Digital (90, 138, 344)-net over F4, using
(90, 138, 9444)-Net in Base 4 — Upper bound on s
There is no (90, 138, 9445)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 121487 505249 196321 765207 031146 464173 116782 011290 425436 580370 003062 464562 813087 084044 > 4138 [i]