Best Known (201, 244, s)-Nets in Base 3
(201, 244, 1480)-Net over F3 — Constructive and digital
Digital (201, 244, 1480)-net over F3, using
- t-expansion [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
(201, 244, 5389)-Net over F3 — Digital
Digital (201, 244, 5389)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3244, 5389, F3, 43) (dual of [5389, 5145, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(3244, 6620, F3, 43) (dual of [6620, 6376, 44]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3241, 6617, F3, 43) (dual of [6617, 6376, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(34) [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(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(316, 56, F3, 7) (dual of [56, 40, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(42) ⊂ Ce(34) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3241, 6617, F3, 43) (dual of [6617, 6376, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(3244, 6620, F3, 43) (dual of [6620, 6376, 44]-code), using
(201, 244, 1440226)-Net in Base 3 — Upper bound on s
There is no (201, 244, 1440227)-net in base 3, because
- 1 times m-reduction [i] would yield (201, 243, 1440227)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 87 189809 245197 905286 042616 329359 895615 668477 733576 971308 110911 365667 470074 937181 931011 855744 494208 546087 311713 236895 > 3243 [i]