Best Known (227−84, 227, s)-Nets in Base 4
(227−84, 227, 147)-Net over F4 — Constructive and digital
Digital (143, 227, 147)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 47, 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 (96, 180, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 90, 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, 90, 65)-net over F16, using
- digital (5, 47, 17)-net over F4, using
(227−84, 227, 152)-Net in Base 4 — Constructive
(143, 227, 152)-net in base 4, using
- 3 times m-reduction [i] based on (143, 230, 152)-net in base 4, using
- trace code for nets [i] based on (28, 115, 76)-net in base 16, using
- base change [i] based on digital (5, 92, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 92, 76)-net over F32, using
- trace code for nets [i] based on (28, 115, 76)-net in base 16, using
(227−84, 227, 425)-Net over F4 — Digital
Digital (143, 227, 425)-net over F4, using
(227−84, 227, 9843)-Net in Base 4 — Upper bound on s
There is no (143, 227, 9844)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 46596 313702 757045 742931 140456 931547 572328 101757 945361 641274 240402 949306 549891 532114 182527 579450 611132 918975 182891 463989 182183 204775 597690 > 4227 [i]