Best Known (24, 33, s)-Nets in Base 49
(24, 33, 1441201)-Net over F49 — Constructive and digital
Digital (24, 33, 1441201)-net over F49, using
- net defined by OOA [i] based on linear OOA(4933, 1441201, F49, 9, 9) (dual of [(1441201, 9), 12970776, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(4933, 5764805, F49, 9) (dual of [5764805, 5764772, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(4933, 5764805, F49, 9) (dual of [5764805, 5764772, 10]-code), using
(24, 33, 3752215)-Net over F49 — Digital
Digital (24, 33, 3752215)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4933, 3752215, F49, 9) (dual of [3752215, 3752182, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using
(24, 33, large)-Net in Base 49 — Upper bound on s
There is no (24, 33, large)-net in base 49, because
- 7 times m-reduction [i] would yield (24, 26, large)-net in base 49, but