Best Known (36, 36+14, s)-Nets in Base 8
(36, 36+14, 586)-Net over F8 — Constructive and digital
Digital (36, 50, 586)-net over F8, using
- net defined by OOA [i] based on linear OOA(850, 586, F8, 14, 14) (dual of [(586, 14), 8154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(850, 4102, F8, 14) (dual of [4102, 4052, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(850, 4105, F8, 14) (dual of [4105, 4055, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(849, 4096, F8, 14) (dual of [4096, 4047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(841, 4096, F8, 12) (dual of [4096, 4055, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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(850, 4105, F8, 14) (dual of [4105, 4055, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(850, 4102, F8, 14) (dual of [4102, 4052, 15]-code), using
(36, 36+14, 3674)-Net over F8 — Digital
Digital (36, 50, 3674)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(850, 3674, F8, 14) (dual of [3674, 3624, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(850, 4105, F8, 14) (dual of [4105, 4055, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(849, 4096, F8, 14) (dual of [4096, 4047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(841, 4096, F8, 12) (dual of [4096, 4055, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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(850, 4105, F8, 14) (dual of [4105, 4055, 15]-code), using
(36, 36+14, 1362894)-Net in Base 8 — Upper bound on s
There is no (36, 50, 1362895)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1427 254607 894837 795622 881878 816597 563284 211584 > 850 [i]