Best Known (111, 111+74, s)-Nets in Base 4
(111, 111+74, 130)-Net over F4 — Constructive and digital
Digital (111, 185, 130)-net over F4, using
- t-expansion [i] based on digital (105, 185, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(111, 111+74, 273)-Net over F4 — Digital
Digital (111, 185, 273)-net over F4, using
(111, 111+74, 4971)-Net in Base 4 — Upper bound on s
There is no (111, 185, 4972)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2420 532005 207491 944998 269994 317649 281860 150103 679075 305913 135770 791039 849061 183915 298333 360015 656170 606134 096230 > 4185 [i]