Best Known (46−14, 46, s)-Nets in Base 49
(46−14, 46, 16810)-Net over F49 — Constructive and digital
Digital (32, 46, 16810)-net over F49, using
- 491 times duplication [i] based on digital (31, 45, 16810)-net over F49, using
- net defined by OOA [i] based on linear OOA(4945, 16810, F49, 14, 14) (dual of [(16810, 14), 235295, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4945, 117670, F49, 14) (dual of [117670, 117625, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4945, 117672, F49, 14) (dual of [117672, 117627, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(495, 23, F49, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4945, 117672, F49, 14) (dual of [117672, 117627, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(4945, 117670, F49, 14) (dual of [117670, 117625, 15]-code), using
- net defined by OOA [i] based on linear OOA(4945, 16810, F49, 14, 14) (dual of [(16810, 14), 235295, 15]-NRT-code), using
(46−14, 46, 117676)-Net over F49 — Digital
Digital (32, 46, 117676)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4946, 117676, F49, 14) (dual of [117676, 117630, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(6) [i] based on
- linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(496, 27, F49, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,49)), using
- discarding factors / shortening the dual code based on linear OA(496, 49, F49, 6) (dual of [49, 43, 7]-code or 49-arc in PG(5,49)), using
- Reed–Solomon code RS(43,49) [i]
- discarding factors / shortening the dual code based on linear OA(496, 49, F49, 6) (dual of [49, 43, 7]-code or 49-arc in PG(5,49)), using
- construction X applied to Ce(13) ⊂ Ce(6) [i] based on
(46−14, 46, large)-Net in Base 49 — Upper bound on s
There is no (32, 46, large)-net in base 49, because
- 12 times m-reduction [i] would yield (32, 34, large)-net in base 49, but