Best Known (88−21, 88, s)-Nets in Base 8
(88−21, 88, 821)-Net over F8 — Constructive and digital
Digital (67, 88, 821)-net over F8, using
- net defined by OOA [i] based on linear OOA(888, 821, F8, 21, 21) (dual of [(821, 21), 17153, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(888, 8211, F8, 21) (dual of [8211, 8123, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(888, 8216, F8, 21) (dual of [8216, 8128, 22]-code), using
- trace code [i] based on linear OA(6444, 4108, F64, 21) (dual of [4108, 4064, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(6441, 4097, F64, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- trace code [i] based on linear OA(6444, 4108, F64, 21) (dual of [4108, 4064, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(888, 8216, F8, 21) (dual of [8216, 8128, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(888, 8211, F8, 21) (dual of [8211, 8123, 22]-code), using
(88−21, 88, 1032)-Net in Base 8 — Constructive
(67, 88, 1032)-net in base 8, using
- base change [i] based on digital (45, 66, 1032)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (12, 22, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 11, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 11, 258)-net over F256, using
- digital (23, 44, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 22, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- trace code for nets [i] based on digital (1, 22, 258)-net over F256, using
- digital (12, 22, 516)-net over F16, using
- (u, u+v)-construction [i] based on
(88−21, 88, 11173)-Net over F8 — Digital
Digital (67, 88, 11173)-net over F8, using
(88−21, 88, large)-Net in Base 8 — Upper bound on s
There is no (67, 88, large)-net in base 8, because
- 19 times m-reduction [i] would yield (67, 69, large)-net in base 8, but