Best Known (38, 43, s)-Nets in Base 3
(38, 43, 2391491)-Net over F3 — Constructive and digital
Digital (38, 43, 2391491)-net over F3, using
- net defined by OOA [i] based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
(38, 43, 4345614)-Net over F3 — Digital
Digital (38, 43, 4345614)-net over F3, using
- net defined by OOA [i] based on linear OOA(343, 4345614, F3, 5, 5) (dual of [(4345614, 5), 21728027, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(343, 4345614, F3, 4, 5) (dual of [(4345614, 4), 17382413, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(343, 4345614, F3, 5) (dual of [4345614, 4345571, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(343, 4345614, F3, 5) (dual of [4345614, 4345571, 6]-code), using
- appending kth column [i] based on linear OOA(343, 4345614, F3, 4, 5) (dual of [(4345614, 4), 17382413, 6]-NRT-code), using
(38, 43, large)-Net in Base 3 — Upper bound on s
There is no (38, 43, large)-net in base 3, because
- 3 times m-reduction [i] would yield (38, 40, large)-net in base 3, but