Best Known (189, 230, s)-Nets in Base 3
(189, 230, 1480)-Net over F3 — Constructive and digital
Digital (189, 230, 1480)-net over F3, using
- 32 times duplication [i] based on digital (187, 228, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 57, 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, 57, 370)-net over F81, using
(189, 230, 4838)-Net over F3 — Digital
Digital (189, 230, 4838)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3230, 4838, F3, 41) (dual of [4838, 4608, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(3230, 6606, F3, 41) (dual of [6606, 6376, 42]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3228, 6604, F3, 41) (dual of [6604, 6376, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3228, 6604, F3, 41) (dual of [6604, 6376, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(3230, 6606, F3, 41) (dual of [6606, 6376, 42]-code), using
(189, 230, 1205889)-Net in Base 3 — Upper bound on s
There is no (189, 230, 1205890)-net in base 3, because
- 1 times m-reduction [i] would yield (189, 229, 1205890)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 18 229284 597602 308501 564778 192863 818042 082691 042923 850182 756542 526418 637466 391751 574618 186142 753374 177114 084809 > 3229 [i]