Best Known (17, 33, s)-Nets in Base 49
(17, 33, 301)-Net over F49 — Constructive and digital
Digital (17, 33, 301)-net over F49, using
- net defined by OOA [i] based on linear OOA(4933, 301, F49, 16, 16) (dual of [(301, 16), 4783, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4933, 2408, F49, 16) (dual of [2408, 2375, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4933, 2409, F49, 16) (dual of [2409, 2376, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [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(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(492, 8, F49, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(4933, 2409, F49, 16) (dual of [2409, 2376, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(4933, 2408, F49, 16) (dual of [2408, 2375, 17]-code), using
(17, 33, 1204)-Net over F49 — Digital
Digital (17, 33, 1204)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4933, 1204, F49, 2, 16) (dual of [(1204, 2), 2375, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4933, 2408, F49, 16) (dual of [2408, 2375, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4933, 2409, F49, 16) (dual of [2409, 2376, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [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(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(492, 8, F49, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(4933, 2409, F49, 16) (dual of [2409, 2376, 17]-code), using
- OOA 2-folding [i] based on linear OA(4933, 2408, F49, 16) (dual of [2408, 2375, 17]-code), using
(17, 33, 735369)-Net in Base 49 — Upper bound on s
There is no (17, 33, 735370)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 59 768721 665187 365494 515972 266543 046551 400264 519565 308673 > 4933 [i]