Best Known (198−34, 198, s)-Nets in Base 3
(198−34, 198, 896)-Net over F3 — Constructive and digital
Digital (164, 198, 896)-net over F3, using
- t-expansion [i] based on digital (163, 198, 896)-net over F3, using
- 2 times m-reduction [i] based on digital (163, 200, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 50, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 50, 224)-net over F81, using
- 2 times m-reduction [i] based on digital (163, 200, 896)-net over F3, using
(198−34, 198, 5505)-Net over F3 — Digital
Digital (164, 198, 5505)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3198, 5505, F3, 34) (dual of [5505, 5307, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3198, 9841, F3, 34) (dual of [9841, 9643, 35]-code), using
(198−34, 198, 1294103)-Net in Base 3 — Upper bound on s
There is no (164, 198, 1294104)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29512 880363 296021 899566 165755 092365 609991 287926 614543 516955 570982 734071 609960 711274 753442 366769 > 3198 [i]