Best Known (252−90, 252, s)-Nets in Base 4
(252−90, 252, 200)-Net over F4 — Constructive and digital
Digital (162, 252, 200)-net over F4, using
- t-expansion [i] based on digital (161, 252, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 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) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(252−90, 252, 208)-Net in Base 4 — Constructive
(162, 252, 208)-net in base 4, using
- 2 times m-reduction [i] based on (162, 254, 208)-net in base 4, using
- trace code for nets [i] based on (35, 127, 104)-net in base 16, using
- 3 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
- 3 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- trace code for nets [i] based on (35, 127, 104)-net in base 16, using
(252−90, 252, 528)-Net over F4 — Digital
Digital (162, 252, 528)-net over F4, using
(252−90, 252, 13785)-Net in Base 4 — Upper bound on s
There is no (162, 252, 13786)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 52 443891 539557 702869 261209 928457 259560 310940 282176 898607 943951 759876 686456 184519 956199 795850 021784 228002 523128 009585 482111 437374 456266 323374 061737 890152 > 4252 [i]