Best Known (256−90, 256, s)-Nets in Base 4
(256−90, 256, 200)-Net over F4 — Constructive and digital
Digital (166, 256, 200)-net over F4, using
- t-expansion [i] based on digital (161, 256, 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
(256−90, 256, 240)-Net in Base 4 — Constructive
(166, 256, 240)-net in base 4, using
- 2 times m-reduction [i] based on (166, 258, 240)-net in base 4, using
- trace code for nets [i] based on (37, 129, 120)-net in base 16, using
- 1 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- 1 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- trace code for nets [i] based on (37, 129, 120)-net in base 16, using
(256−90, 256, 567)-Net over F4 — Digital
Digital (166, 256, 567)-net over F4, using
(256−90, 256, 15598)-Net in Base 4 — Upper bound on s
There is no (166, 256, 15599)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13435 614071 663421 065557 612811 395298 053957 035367 718979 726957 469179 464885 786735 279180 113309 029847 429960 844309 038944 423046 733459 012105 899459 694875 903685 921458 > 4256 [i]