Best Known (36, 36+10, s)-Nets in Base 3
(36, 36+10, 440)-Net over F3 — Constructive and digital
Digital (36, 46, 440)-net over F3, using
- net defined by OOA [i] based on linear OOA(346, 440, F3, 10, 10) (dual of [(440, 10), 4354, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(346, 2200, F3, 10) (dual of [2200, 2154, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(343, 2187, F3, 10) (dual of [2187, 2144, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(329, 2187, F3, 7) (dual of [2187, 2158, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- OA 5-folding and stacking [i] based on linear OA(346, 2200, F3, 10) (dual of [2200, 2154, 11]-code), using
(36, 36+10, 1100)-Net over F3 — Digital
Digital (36, 46, 1100)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(346, 1100, F3, 2, 10) (dual of [(1100, 2), 2154, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(346, 2200, F3, 10) (dual of [2200, 2154, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(343, 2187, F3, 10) (dual of [2187, 2144, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(329, 2187, F3, 7) (dual of [2187, 2158, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(346, 2200, F3, 10) (dual of [2200, 2154, 11]-code), using
(36, 36+10, 31934)-Net in Base 3 — Upper bound on s
There is no (36, 46, 31935)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8863 582266 822711 759735 > 346 [i]