Best Known (200, 242, s)-Nets in Base 3
(200, 242, 1480)-Net over F3 — Constructive and digital
Digital (200, 242, 1480)-net over F3, using
- t-expansion [i] based on digital (199, 242, 1480)-net over F3, using
- 2 times m-reduction [i] based on digital (199, 244, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 61, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 61, 370)-net over F81, using
- 2 times m-reduction [i] based on digital (199, 244, 1480)-net over F3, using
(200, 242, 5869)-Net over F3 — Digital
Digital (200, 242, 5869)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3242, 5869, F3, 42) (dual of [5869, 5627, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3242, 6626, F3, 42) (dual of [6626, 6384, 43]-code), using
- construction X applied to Ce(42) ⊂ Ce(33) [i] based on
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(317, 65, F3, 7) (dual of [65, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- construction X applied to Ce(42) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(3242, 6626, F3, 42) (dual of [6626, 6384, 43]-code), using
(200, 242, 1366817)-Net in Base 3 — Upper bound on s
There is no (200, 242, 1366818)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29 063456 452452 922718 173606 483846 341619 145424 377862 667238 699467 973920 556438 517673 984071 297472 354700 828162 771302 798781 > 3242 [i]