Best Known (87, 109, s)-Nets in Base 8
(87, 109, 2996)-Net over F8 — Constructive and digital
Digital (87, 109, 2996)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-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 (2, 13, 17)-net over F8, using
(87, 109, 5958)-Net in Base 8 — Constructive
(87, 109, 5958)-net in base 8, using
- 81 times duplication [i] based on (86, 108, 5958)-net in base 8, using
- base change [i] based on digital (59, 81, 5958)-net over F16, using
- net defined by OOA [i] based on linear OOA(1681, 5958, F16, 22, 22) (dual of [(5958, 22), 130995, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(1681, 65538, F16, 22) (dual of [65538, 65457, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(1681, 65540, F16, 22) (dual of [65540, 65459, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [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(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(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 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(1681, 65540, F16, 22) (dual of [65540, 65459, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(1681, 65538, F16, 22) (dual of [65538, 65457, 23]-code), using
- net defined by OOA [i] based on linear OOA(1681, 5958, F16, 22, 22) (dual of [(5958, 22), 130995, 23]-NRT-code), using
- base change [i] based on digital (59, 81, 5958)-net over F16, using
(87, 109, 60386)-Net over F8 — Digital
Digital (87, 109, 60386)-net over F8, using
(87, 109, large)-Net in Base 8 — Upper bound on s
There is no (87, 109, large)-net in base 8, because
- 20 times m-reduction [i] would yield (87, 89, large)-net in base 8, but