Best Known (10, 18, s)-Nets in Base 49
(10, 18, 603)-Net over F49 — Constructive and digital
Digital (10, 18, 603)-net over F49, using
- net defined by OOA [i] based on linear OOA(4918, 603, F49, 8, 8) (dual of [(603, 8), 4806, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(4918, 2412, F49, 8) (dual of [2412, 2394, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- 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(497, 2401, F49, 4) (dual of [2401, 2394, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(7) ⊂ Ce(3) [i] based on
- OA 4-folding and stacking [i] based on linear OA(4918, 2412, F49, 8) (dual of [2412, 2394, 9]-code), using
(10, 18, 2514)-Net over F49 — Digital
Digital (10, 18, 2514)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4918, 2514, F49, 8) (dual of [2514, 2496, 9]-code), using
- 108 step Varšamov–Edel lengthening with (ri) = (2, 12 times 0, 1, 94 times 0) [i] based on linear OA(4915, 2403, F49, 8) (dual of [2403, 2388, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- 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(4913, 2401, F49, 7) (dual of [2401, 2388, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 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(7) ⊂ Ce(6) [i] based on
- 108 step Varšamov–Edel lengthening with (ri) = (2, 12 times 0, 1, 94 times 0) [i] based on linear OA(4915, 2403, F49, 8) (dual of [2403, 2388, 9]-code), using
(10, 18, 1860773)-Net in Base 49 — Upper bound on s
There is no (10, 18, 1860774)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 2 651732 446305 601608 442907 937409 > 4918 [i]