Best Known (94, 94+12, s)-Nets in Base 3
(94, 94+12, 265725)-Net over F3 — Constructive and digital
Digital (94, 106, 265725)-net over F3, using
- net defined by OOA [i] based on linear OOA(3106, 265725, F3, 12, 12) (dual of [(265725, 12), 3188594, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3106, 1594350, F3, 12) (dual of [1594350, 1594244, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(31, 27, F3, 1) (dual of [27, 26, 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(12) ⊂ Ce(9) [i] based on
- OA 6-folding and stacking [i] based on linear OA(3106, 1594350, F3, 12) (dual of [1594350, 1594244, 13]-code), using
(94, 94+12, 676266)-Net over F3 — Digital
Digital (94, 106, 676266)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3106, 676266, F3, 2, 12) (dual of [(676266, 2), 1352426, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3106, 797175, F3, 2, 12) (dual of [(797175, 2), 1594244, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3106, 1594350, F3, 12) (dual of [1594350, 1594244, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(31, 27, F3, 1) (dual of [27, 26, 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(12) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(3106, 1594350, F3, 12) (dual of [1594350, 1594244, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(3106, 797175, F3, 2, 12) (dual of [(797175, 2), 1594244, 13]-NRT-code), using
(94, 94+12, large)-Net in Base 3 — Upper bound on s
There is no (94, 106, large)-net in base 3, because
- 10 times m-reduction [i] would yield (94, 96, large)-net in base 3, but