Best Known (35, 35+16, s)-Nets in Base 49
(35, 35+16, 14709)-Net over F49 — Constructive and digital
Digital (35, 51, 14709)-net over F49, using
- net defined by OOA [i] based on linear OOA(4951, 14709, F49, 16, 16) (dual of [(14709, 16), 235293, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4951, 117672, F49, 16) (dual of [117672, 117621, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(4946, 117649, F49, 16) (dual of [117649, 117603, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(15) ⊂ Ce(9) [i] based on
- OA 8-folding and stacking [i] based on linear OA(4951, 117672, F49, 16) (dual of [117672, 117621, 17]-code), using
(35, 35+16, 117672)-Net over F49 — Digital
Digital (35, 51, 117672)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4951, 117672, F49, 16) (dual of [117672, 117621, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(4946, 117649, F49, 16) (dual of [117649, 117603, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(15) ⊂ Ce(9) [i] based on
(35, 35+16, large)-Net in Base 49 — Upper bound on s
There is no (35, 51, large)-net in base 49, because
- 14 times m-reduction [i] would yield (35, 37, large)-net in base 49, but