Best Known (162−102, 162, s)-Nets in Base 4
(162−102, 162, 66)-Net over F4 — Constructive and digital
Digital (60, 162, 66)-net over F4, using
- t-expansion [i] based on digital (49, 162, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(162−102, 162, 91)-Net over F4 — Digital
Digital (60, 162, 91)-net over F4, using
- t-expansion [i] based on digital (50, 162, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(162−102, 162, 500)-Net in Base 4 — Upper bound on s
There is no (60, 162, 501)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 37 021590 793700 555983 825369 171729 668935 093148 665522 035837 677836 962600 337665 599091 893451 748768 802364 > 4162 [i]