Best Known (244−61, 244, s)-Nets in Base 3
(244−61, 244, 328)-Net over F3 — Constructive and digital
Digital (183, 244, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 61, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(244−61, 244, 1002)-Net over F3 — Digital
Digital (183, 244, 1002)-net over F3, using
(244−61, 244, 44070)-Net in Base 3 — Upper bound on s
There is no (183, 244, 44071)-net in base 3, because
- 1 times m-reduction [i] would yield (183, 243, 44071)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 87 205276 170812 597976 496232 414183 570787 273796 290232 869378 283128 767985 772635 304394 842999 094494 690968 887397 225225 959637 > 3243 [i]