Best Known (62, 171, s)-Nets in Base 4
(62, 171, 66)-Net over F4 — Constructive and digital
Digital (62, 171, 66)-net over F4, using
- t-expansion [i] based on digital (49, 171, 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
(62, 171, 99)-Net over F4 — Digital
Digital (62, 171, 99)-net over F4, using
- t-expansion [i] based on digital (61, 171, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(62, 171, 506)-Net in Base 4 — Upper bound on s
There is no (62, 171, 507)-net in base 4, because
- 1 times m-reduction [i] would yield (62, 170, 507)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 446091 411796 868535 023132 768258 570237 910488 948280 152839 913388 504149 613135 994424 499376 369663 949143 684994 > 4170 [i]