Best Known (147, 147+85, s)-Nets in Base 4
(147, 147+85, 151)-Net over F4 — Constructive and digital
Digital (147, 232, 151)-net over F4, using
- 41 times duplication [i] based on digital (146, 231, 151)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 49, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (97, 182, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 91, 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, 91, 65)-net over F16, using
- digital (7, 49, 21)-net over F4, using
- (u, u+v)-construction [i] based on
(147, 147+85, 196)-Net in Base 4 — Constructive
(147, 232, 196)-net in base 4, using
- 42 times duplication [i] based on (145, 230, 196)-net in base 4, using
- trace code for nets [i] based on (30, 115, 98)-net in base 16, using
- base change [i] based on digital (7, 92, 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, 92, 98)-net over F32, using
- trace code for nets [i] based on (30, 115, 98)-net in base 16, using
(147, 147+85, 449)-Net over F4 — Digital
Digital (147, 232, 449)-net over F4, using
(147, 147+85, 11237)-Net in Base 4 — Upper bound on s
There is no (147, 232, 11238)-net in base 4, because
- 1 times m-reduction [i] would yield (147, 231, 11238)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 917889 720234 077802 668748 140916 061706 450667 546965 768215 929633 401557 562114 080810 661621 153127 340511 685601 286306 385249 948938 913487 092636 648560 > 4231 [i]