Best Known (17, 17+8, s)-Nets in Base 49
(17, 17+8, 29416)-Net over F49 — Constructive and digital
Digital (17, 25, 29416)-net over F49, using
- net defined by OOA [i] based on linear OOA(4925, 29416, F49, 8, 8) (dual of [(29416, 8), 235303, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(4925, 117664, F49, 8) (dual of [117664, 117639, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- 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(4910, 117649, F49, 4) (dual of [117649, 117639, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(493, 15, F49, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,49) or 15-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- OA 4-folding and stacking [i] based on linear OA(4925, 117664, F49, 8) (dual of [117664, 117639, 9]-code), using
(17, 17+8, 117664)-Net over F49 — Digital
Digital (17, 25, 117664)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4925, 117664, F49, 8) (dual of [117664, 117639, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- 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(4910, 117649, F49, 4) (dual of [117649, 117639, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(493, 15, F49, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,49) or 15-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
(17, 17+8, large)-Net in Base 49 — Upper bound on s
There is no (17, 25, large)-net in base 49, because
- 6 times m-reduction [i] would yield (17, 19, large)-net in base 49, but