Best Known (163, 163+90, s)-Nets in Base 4
(163, 163+90, 200)-Net over F4 — Constructive and digital
Digital (163, 253, 200)-net over F4, using
- t-expansion [i] based on digital (161, 253, 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
(163, 163+90, 208)-Net in Base 4 — Constructive
(163, 253, 208)-net in base 4, using
- 3 times m-reduction [i] based on (163, 256, 208)-net in base 4, using
- trace code for nets [i] based on (35, 128, 104)-net in base 16, using
- 2 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
- 2 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- trace code for nets [i] based on (35, 128, 104)-net in base 16, using
(163, 163+90, 538)-Net over F4 — Digital
Digital (163, 253, 538)-net over F4, using
(163, 163+90, 14218)-Net in Base 4 — Upper bound on s
There is no (163, 253, 14219)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 210 131012 080912 966251 783606 709578 558881 102801 158820 600483 137667 256456 447011 639472 733741 966552 106420 003110 046613 059308 119609 111480 085437 502771 057245 698752 > 4253 [i]