Best Known (12, 12+10, s)-Nets in Base 49
(12, 12+10, 482)-Net over F49 — Constructive and digital
Digital (12, 22, 482)-net over F49, using
- net defined by OOA [i] based on linear OOA(4922, 482, F49, 10, 10) (dual of [(482, 10), 4798, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4922, 2410, F49, 10) (dual of [2410, 2388, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4922, 2412, F49, 10) (dual of [2412, 2390, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- 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(4911, 2401, F49, 6) (dual of [2401, 2390, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(493, 11, F49, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,49) or 11-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(9) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4922, 2412, F49, 10) (dual of [2412, 2390, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(4922, 2410, F49, 10) (dual of [2410, 2388, 11]-code), using
(12, 12+10, 2141)-Net over F49 — Digital
Digital (12, 22, 2141)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4922, 2141, F49, 10) (dual of [2141, 2119, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4922, 2412, F49, 10) (dual of [2412, 2390, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- 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(4911, 2401, F49, 6) (dual of [2401, 2390, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(493, 11, F49, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,49) or 11-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(9) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4922, 2412, F49, 10) (dual of [2412, 2390, 11]-code), using
(12, 12+10, 1484079)-Net in Base 49 — Upper bound on s
There is no (12, 22, 1484080)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 15 286729 531558 270205 052447 438083 935489 > 4922 [i]