Best Known (33, 48, s)-Nets in Base 49
(33, 48, 16810)-Net over F49 — Constructive and digital
Digital (33, 48, 16810)-net over F49, using
- net defined by OOA [i] based on linear OOA(4948, 16810, F49, 15, 15) (dual of [(16810, 15), 252102, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4948, 117671, F49, 15) (dual of [117671, 117623, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4948, 117673, F49, 15) (dual of [117673, 117625, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(4925, 117650, F49, 9) (dual of [117650, 117625, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [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 C([0,7]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4948, 117673, F49, 15) (dual of [117673, 117625, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4948, 117671, F49, 15) (dual of [117671, 117623, 16]-code), using
(33, 48, 117673)-Net over F49 — Digital
Digital (33, 48, 117673)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4948, 117673, F49, 15) (dual of [117673, 117625, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(4925, 117650, F49, 9) (dual of [117650, 117625, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [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 C([0,7]) ⊂ C([0,4]) [i] based on
(33, 48, large)-Net in Base 49 — Upper bound on s
There is no (33, 48, large)-net in base 49, because
- 13 times m-reduction [i] would yield (33, 35, large)-net in base 49, but