Best Known (119, 119+19, s)-Nets in Base 3
(119, 119+19, 19685)-Net over F3 — Constructive and digital
Digital (119, 138, 19685)-net over F3, using
- 31 times duplication [i] based on digital (118, 137, 19685)-net over F3, using
- net defined by OOA [i] based on linear OOA(3137, 19685, F3, 19, 19) (dual of [(19685, 19), 373878, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3137, 177166, F3, 19) (dual of [177166, 177029, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3137, 177173, F3, 19) (dual of [177173, 177036, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(34, 26, F3, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3137, 177173, F3, 19) (dual of [177173, 177036, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3137, 177166, F3, 19) (dual of [177166, 177029, 20]-code), using
- net defined by OOA [i] based on linear OOA(3137, 19685, F3, 19, 19) (dual of [(19685, 19), 373878, 20]-NRT-code), using
(119, 119+19, 59058)-Net over F3 — Digital
Digital (119, 138, 59058)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3138, 59058, F3, 3, 19) (dual of [(59058, 3), 177036, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3138, 177174, F3, 19) (dual of [177174, 177036, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3137, 177173, F3, 19) (dual of [177173, 177036, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(34, 26, F3, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3137, 177173, F3, 19) (dual of [177173, 177036, 20]-code), using
- OOA 3-folding [i] based on linear OA(3138, 177174, F3, 19) (dual of [177174, 177036, 20]-code), using
(119, 119+19, large)-Net in Base 3 — Upper bound on s
There is no (119, 138, large)-net in base 3, because
- 17 times m-reduction [i] would yield (119, 121, large)-net in base 3, but