Best Known (14, 26, s)-Nets in Base 49
(14, 26, 402)-Net over F49 — Constructive and digital
Digital (14, 26, 402)-net over F49, using
- net defined by OOA [i] based on linear OOA(4926, 402, F49, 12, 12) (dual of [(402, 12), 4798, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4926, 2412, F49, 12) (dual of [2412, 2386, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(11) ⊂ Ce(7) [i] based on
- OA 6-folding and stacking [i] based on linear OA(4926, 2412, F49, 12) (dual of [2412, 2386, 13]-code), using
(14, 26, 1582)-Net over F49 — Digital
Digital (14, 26, 1582)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4926, 1582, F49, 12) (dual of [1582, 1556, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4926, 2412, F49, 12) (dual of [2412, 2386, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4926, 2412, F49, 12) (dual of [2412, 2386, 13]-code), using
(14, 26, 1315718)-Net in Base 49 — Upper bound on s
There is no (14, 26, 1315719)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 88 124974 493792 598313 278032 410898 695665 843169 > 4926 [i]