Best Known (19, 29, s)-Nets in Base 49
(19, 29, 23531)-Net over F49 — Constructive and digital
Digital (19, 29, 23531)-net over F49, using
- net defined by OOA [i] based on linear OOA(4929, 23531, F49, 10, 10) (dual of [(23531, 10), 235281, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4929, 117655, F49, 10) (dual of [117655, 117626, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 117656, F49, 10) (dual of [117656, 117627, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4929, 117656, F49, 10) (dual of [117656, 117627, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(4929, 117655, F49, 10) (dual of [117655, 117626, 11]-code), using
(19, 29, 64582)-Net over F49 — Digital
Digital (19, 29, 64582)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4929, 64582, F49, 10) (dual of [64582, 64553, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 117656, F49, 10) (dual of [117656, 117627, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4929, 117656, F49, 10) (dual of [117656, 117627, 11]-code), using
(19, 29, large)-Net in Base 49 — Upper bound on s
There is no (19, 29, large)-net in base 49, because
- 8 times m-reduction [i] would yield (19, 21, large)-net in base 49, but