Best Known (185, 185+44, s)-Nets in Base 3
(185, 185+44, 896)-Net over F3 — Constructive and digital
Digital (185, 229, 896)-net over F3, using
- 31 times duplication [i] based on digital (184, 228, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 57, 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, 57, 224)-net over F81, using
(185, 185+44, 3173)-Net over F3 — Digital
Digital (185, 229, 3173)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3229, 3173, F3, 44) (dual of [3173, 2944, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3229, 3281, F3, 44) (dual of [3281, 3052, 45]-code), using
- an extension Ce(43) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- discarding factors / shortening the dual code based on linear OA(3229, 3281, F3, 44) (dual of [3281, 3052, 45]-code), using
(185, 185+44, 418985)-Net in Base 3 — Upper bound on s
There is no (185, 229, 418986)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 18 229419 043300 695493 654233 558521 180568 788948 268318 387849 800508 615760 023883 965775 386840 517073 613608 439048 687181 > 3229 [i]