Best Known (17, 24, s)-Nets in Base 49
(17, 24, 45167)-Net over F49 — Constructive and digital
Digital (17, 24, 45167)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 5950)-net over F49, using
- net defined by OOA [i] based on linear OOA(495, 5950, F49, 3, 3) (dual of [(5950, 3), 17845, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(495, 5950, F49, 2, 3) (dual of [(5950, 2), 11895, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(495, 5950, F49, 3, 3) (dual of [(5950, 3), 17845, 4]-NRT-code), using
- digital (12, 19, 39217)-net over F49, using
- net defined by OOA [i] based on linear OOA(4919, 39217, F49, 7, 7) (dual of [(39217, 7), 274500, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(4919, 117652, F49, 7) (dual of [117652, 117633, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(4919, 117649, F49, 7) (dual of [117649, 117630, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(4919, 117652, F49, 7) (dual of [117652, 117633, 8]-code), using
- net defined by OOA [i] based on linear OOA(4919, 39217, F49, 7, 7) (dual of [(39217, 7), 274500, 8]-NRT-code), using
- digital (2, 5, 5950)-net over F49, using
(17, 24, 359558)-Net over F49 — Digital
Digital (17, 24, 359558)-net over F49, using
(17, 24, large)-Net in Base 49 — Upper bound on s
There is no (17, 24, large)-net in base 49, because
- 5 times m-reduction [i] would yield (17, 19, large)-net in base 49, but