Best Known (90, 90+22, s)-Nets in Base 8
(90, 90+22, 3007)-Net over F8 — Constructive and digital
Digital (90, 112, 3007)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 16, 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 (74, 96, 2979)-net over F8, using
- net defined by OOA [i] based on linear OOA(896, 2979, F8, 22, 22) (dual of [(2979, 22), 65442, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(896, 32769, F8, 22) (dual of [32769, 32673, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(896, 32773, F8, 22) (dual of [32773, 32677, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(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(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(896, 32773, F8, 22) (dual of [32773, 32677, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(896, 32769, F8, 22) (dual of [32769, 32673, 23]-code), using
- net defined by OOA [i] based on linear OOA(896, 2979, F8, 22, 22) (dual of [(2979, 22), 65442, 23]-NRT-code), using
- digital (5, 16, 28)-net over F8, using
(90, 90+22, 5959)-Net in Base 8 — Constructive
(90, 112, 5959)-net in base 8, using
- base change [i] based on digital (62, 84, 5959)-net over F16, using
- 161 times duplication [i] based on digital (61, 83, 5959)-net over F16, using
- net defined by OOA [i] based on linear OOA(1683, 5959, F16, 22, 22) (dual of [(5959, 22), 131015, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(1683, 65549, F16, 22) (dual of [65549, 65466, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(1683, 65550, F16, 22) (dual of [65550, 65467, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(1683, 65550, F16, 22) (dual of [65550, 65467, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(1683, 65549, F16, 22) (dual of [65549, 65466, 23]-code), using
- net defined by OOA [i] based on linear OOA(1683, 5959, F16, 22, 22) (dual of [(5959, 22), 131015, 23]-NRT-code), using
- 161 times duplication [i] based on digital (61, 83, 5959)-net over F16, using
(90, 90+22, 81270)-Net over F8 — Digital
Digital (90, 112, 81270)-net over F8, using
(90, 90+22, large)-Net in Base 8 — Upper bound on s
There is no (90, 112, large)-net in base 8, because
- 20 times m-reduction [i] would yield (90, 92, large)-net in base 8, but