Best Known (71, 92, s)-Nets in Base 8
(71, 92, 3277)-Net over F8 — Constructive and digital
Digital (71, 92, 3277)-net over F8, using
- 81 times duplication [i] based on digital (70, 91, 3277)-net over F8, using
- net defined by OOA [i] based on linear OOA(891, 3277, F8, 21, 21) (dual of [(3277, 21), 68726, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(891, 32771, F8, 21) (dual of [32771, 32680, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(891, 32773, F8, 21) (dual of [32773, 32682, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(891, 32768, F8, 21) (dual of [32768, 32677, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(891, 32773, F8, 21) (dual of [32773, 32682, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(891, 32771, F8, 21) (dual of [32771, 32680, 22]-code), using
- net defined by OOA [i] based on linear OOA(891, 3277, F8, 21, 21) (dual of [(3277, 21), 68726, 22]-NRT-code), using
(71, 92, 23946)-Net over F8 — Digital
Digital (71, 92, 23946)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(892, 23946, F8, 21) (dual of [23946, 23854, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(892, 32780, F8, 21) (dual of [32780, 32688, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(891, 32769, F8, 21) (dual of [32769, 32678, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(881, 32769, F8, 19) (dual of [32769, 32688, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(892, 32780, F8, 21) (dual of [32780, 32688, 22]-code), using
(71, 92, large)-Net in Base 8 — Upper bound on s
There is no (71, 92, large)-net in base 8, because
- 19 times m-reduction [i] would yield (71, 73, large)-net in base 8, but