Best Known (174, 174+28, s)-Nets in Base 3
(174, 174+28, 12654)-Net over F3 — Constructive and digital
Digital (174, 202, 12654)-net over F3, using
- 32 times duplication [i] based on digital (172, 200, 12654)-net over F3, using
- net defined by OOA [i] based on linear OOA(3200, 12654, F3, 28, 28) (dual of [(12654, 28), 354112, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3200, 177156, F3, 28) (dual of [177156, 176956, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3200, 177159, F3, 28) (dual of [177159, 176959, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3200, 177159, F3, 28) (dual of [177159, 176959, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3200, 177156, F3, 28) (dual of [177156, 176956, 29]-code), using
- net defined by OOA [i] based on linear OOA(3200, 12654, F3, 28, 28) (dual of [(12654, 28), 354112, 29]-NRT-code), using
(174, 174+28, 44290)-Net over F3 — Digital
Digital (174, 202, 44290)-net over F3, using
- 31 times duplication [i] based on digital (173, 201, 44290)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 44290, F3, 4, 28) (dual of [(44290, 4), 176959, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3201, 177160, F3, 28) (dual of [177160, 176959, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3200, 177159, F3, 28) (dual of [177159, 176959, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3200, 177159, F3, 28) (dual of [177159, 176959, 29]-code), using
- OOA 4-folding [i] based on linear OA(3201, 177160, F3, 28) (dual of [177160, 176959, 29]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 44290, F3, 4, 28) (dual of [(44290, 4), 176959, 29]-NRT-code), using
(174, 174+28, large)-Net in Base 3 — Upper bound on s
There is no (174, 202, large)-net in base 3, because
- 26 times m-reduction [i] would yield (174, 176, large)-net in base 3, but