Best Known (34, 46, s)-Nets in Base 27
(34, 46, 88575)-Net over F27 — Constructive and digital
Digital (34, 46, 88575)-net over F27, using
- net defined by OOA [i] based on linear OOA(2746, 88575, F27, 12, 12) (dual of [(88575, 12), 1062854, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2746, 531450, F27, 12) (dual of [531450, 531404, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(2745, 531441, F27, 12) (dual of [531441, 531396, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2737, 531441, F27, 10) (dual of [531441, 531404, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- OA 6-folding and stacking [i] based on linear OA(2746, 531450, F27, 12) (dual of [531450, 531404, 13]-code), using
(34, 46, 480990)-Net over F27 — Digital
Digital (34, 46, 480990)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2746, 480990, F27, 12) (dual of [480990, 480944, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2746, 531450, F27, 12) (dual of [531450, 531404, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(2745, 531441, F27, 12) (dual of [531441, 531396, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2737, 531441, F27, 10) (dual of [531441, 531404, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(2746, 531450, F27, 12) (dual of [531450, 531404, 13]-code), using
(34, 46, large)-Net in Base 27 — Upper bound on s
There is no (34, 46, large)-net in base 27, because
- 10 times m-reduction [i] would yield (34, 36, large)-net in base 27, but