Best Known (109, 109+27, s)-Nets in Base 8
(109, 109+27, 2554)-Net over F8 — Constructive and digital
Digital (109, 136, 2554)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (89, 116, 2520)-net over F8, using
- net defined by OOA [i] based on linear OOA(8116, 2520, F8, 27, 27) (dual of [(2520, 27), 67924, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8116, 32761, F8, 27) (dual of [32761, 32645, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8116, 32761, F8, 27) (dual of [32761, 32645, 28]-code), using
- net defined by OOA [i] based on linear OOA(8116, 2520, F8, 27, 27) (dual of [(2520, 27), 67924, 28]-NRT-code), using
- digital (7, 20, 34)-net over F8, using
(109, 109+27, 5041)-Net in Base 8 — Constructive
(109, 136, 5041)-net in base 8, using
- base change [i] based on digital (75, 102, 5041)-net over F16, using
- 161 times duplication [i] based on digital (74, 101, 5041)-net over F16, using
- net defined by OOA [i] based on linear OOA(16101, 5041, F16, 27, 27) (dual of [(5041, 27), 136006, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16101, 65534, F16, 27) (dual of [65534, 65433, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16101, 65534, F16, 27) (dual of [65534, 65433, 28]-code), using
- net defined by OOA [i] based on linear OOA(16101, 5041, F16, 27, 27) (dual of [(5041, 27), 136006, 28]-NRT-code), using
- 161 times duplication [i] based on digital (74, 101, 5041)-net over F16, using
(109, 109+27, 79822)-Net over F8 — Digital
Digital (109, 136, 79822)-net over F8, using
(109, 109+27, large)-Net in Base 8 — Upper bound on s
There is no (109, 136, large)-net in base 8, because
- 25 times m-reduction [i] would yield (109, 111, large)-net in base 8, but