Best Known (33−7, 33, s)-Nets in Base 49
(33−7, 33, 3843207)-Net over F49 — Constructive and digital
Digital (26, 33, 3843207)-net over F49, using
- net defined by OOA [i] based on linear OOA(4933, 3843207, F49, 9, 7) (dual of [(3843207, 9), 34588830, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(4933, 3843208, F49, 3, 7) (dual of [(3843208, 3), 11529591, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(497, 5769603, F49, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(497, 5769603, F49, 2, 3) (dual of [(5769603, 2), 11539199, 4]-NRT-code), using
- linear OOA(4926, 1921604, F49, 3, 7) (dual of [(1921604, 3), 5764786, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4926, 5764812, F49, 7) (dual of [5764812, 5764786, 8]-code), using
- construction X4 applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(4925, 5764802, F49, 7) (dual of [5764802, 5764777, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(4917, 5764802, F49, 5) (dual of [5764802, 5764785, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(499, 10, F49, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,49)), using
- dual of repetition code with length 10 [i]
- linear OA(491, 10, F49, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- Reed–Solomon code RS(48,49) [i]
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- construction X4 applied to C([0,3]) ⊂ C([0,2]) [i] based on
- OOA 3-folding [i] based on linear OA(4926, 5764812, F49, 7) (dual of [5764812, 5764786, 8]-code), using
- linear OOA(497, 5769603, F49, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(4933, 3843208, F49, 3, 7) (dual of [(3843208, 3), 11529591, 8]-NRT-code), using
(33−7, 33, large)-Net over F49 — Digital
Digital (26, 33, large)-net over F49, using
- 1 times m-reduction [i] based on digital (26, 34, large)-net over F49, using
(33−7, 33, large)-Net in Base 49 — Upper bound on s
There is no (26, 33, large)-net in base 49, because
- 5 times m-reduction [i] would yield (26, 28, large)-net in base 49, but