Best Known (254−93, 254, s)-Nets in Base 4
(254−93, 254, 200)-Net over F4 — Constructive and digital
Digital (161, 254, 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
(254−93, 254, 487)-Net over F4 — Digital
Digital (161, 254, 487)-net over F4, using
(254−93, 254, 12249)-Net in Base 4 — Upper bound on s
There is no (161, 254, 12250)-net in base 4, because
- 1 times m-reduction [i] would yield (161, 253, 12250)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 210 280974 688211 241413 401792 867488 862532 545651 942556 239348 034446 781272 953713 655609 564895 708832 946847 483724 965347 073022 881412 721183 789015 922226 411513 870896 > 4253 [i]