Best Known (20, 20+16, s)-Nets in Base 49
(20, 20+16, 302)-Net over F49 — Constructive and digital
Digital (20, 36, 302)-net over F49, using
- net defined by OOA [i] based on linear OOA(4936, 302, F49, 16, 16) (dual of [(302, 16), 4796, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4936, 2416, F49, 16) (dual of [2416, 2380, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4936, 2418, F49, 16) (dual of [2418, 2382, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(495, 17, F49, 5) (dual of [17, 12, 6]-code or 17-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
- discarding factors / shortening the dual code based on linear OA(4936, 2418, F49, 16) (dual of [2418, 2382, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(4936, 2416, F49, 16) (dual of [2416, 2380, 17]-code), using
(20, 20+16, 2111)-Net over F49 — Digital
Digital (20, 36, 2111)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4936, 2111, F49, 16) (dual of [2111, 2075, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4936, 2418, F49, 16) (dual of [2418, 2382, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(495, 17, F49, 5) (dual of [17, 12, 6]-code or 17-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
- discarding factors / shortening the dual code based on linear OA(4936, 2418, F49, 16) (dual of [2418, 2382, 17]-code), using
(20, 20+16, 3164686)-Net in Base 49 — Upper bound on s
There is no (20, 36, 3164687)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 7 031686 587641 570140 223766 296123 070372 980013 421723 597361 460865 > 4936 [i]