Best Known (86, 107, s)-Nets in Base 8
(86, 107, 3305)-Net over F8 — Constructive and digital
Digital (86, 107, 3305)-net over F8, using
- 81 times duplication [i] based on digital (85, 106, 3305)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- 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
- digital (5, 15, 28)-net over F8, using
- (u, u+v)-construction [i] based on
(86, 107, 6555)-Net in Base 8 — Constructive
(86, 107, 6555)-net in base 8, using
- net defined by OOA [i] based on OOA(8107, 6555, S8, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(8107, 65551, S8, 21), using
- discarding factors based on OA(8107, 65554, S8, 21), using
- discarding parts of the base [i] based on linear OA(1680, 65554, F16, 21) (dual of [65554, 65474, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(1677, 65536, F16, 21) (dual of [65536, 65459, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding parts of the base [i] based on linear OA(1680, 65554, F16, 21) (dual of [65554, 65474, 22]-code), using
- discarding factors based on OA(8107, 65554, S8, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(8107, 65551, S8, 21), using
(86, 107, 80499)-Net over F8 — Digital
Digital (86, 107, 80499)-net over F8, using
(86, 107, large)-Net in Base 8 — Upper bound on s
There is no (86, 107, large)-net in base 8, because
- 19 times m-reduction [i] would yield (86, 88, large)-net in base 8, but