Best Known (62, 74, s)-Nets in Base 8
(62, 74, 349529)-Net over F8 — Constructive and digital
Digital (62, 74, 349529)-net over F8, using
- net defined by OOA [i] based on linear OOA(874, 349529, F8, 12, 12) (dual of [(349529, 12), 4194274, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(874, 2097174, F8, 12) (dual of [2097174, 2097100, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(874, 2097174, F8, 12) (dual of [2097174, 2097100, 13]-code), using
(62, 74, 2097176)-Net over F8 — Digital
Digital (62, 74, 2097176)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
(62, 74, large)-Net in Base 8 — Upper bound on s
There is no (62, 74, large)-net in base 8, because
- 10 times m-reduction [i] would yield (62, 64, large)-net in base 8, but