Best Known (36, 36+14, s)-Nets in Base 9
(36, 36+14, 938)-Net over F9 — Constructive and digital
Digital (36, 50, 938)-net over F9, using
- net defined by OOA [i] based on linear OOA(950, 938, F9, 14, 14) (dual of [(938, 14), 13082, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(950, 6566, F9, 14) (dual of [6566, 6516, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(950, 6570, F9, 14) (dual of [6570, 6520, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(941, 6561, F9, 12) (dual of [6561, 6520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(950, 6570, F9, 14) (dual of [6570, 6520, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(950, 6566, F9, 14) (dual of [6566, 6516, 15]-code), using
(36, 36+14, 5203)-Net over F9 — Digital
Digital (36, 50, 5203)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(950, 5203, F9, 14) (dual of [5203, 5153, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(950, 6570, F9, 14) (dual of [6570, 6520, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(941, 6561, F9, 12) (dual of [6561, 6520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(950, 6570, F9, 14) (dual of [6570, 6520, 15]-code), using
(36, 36+14, 2765960)-Net in Base 9 — Upper bound on s
There is no (36, 50, 2765961)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 515378 144266 901830 013869 588242 280965 288762 001465 > 950 [i]