Best Known (115−23, 115, s)-Nets in Base 8
(115−23, 115, 3003)-Net over F8 — Constructive and digital
Digital (92, 115, 3003)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (78, 101, 2979)-net over F8, using
- net defined by OOA [i] based on linear OOA(8101, 2979, F8, 23, 23) (dual of [(2979, 23), 68416, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8101, 32770, F8, 23) (dual of [32770, 32669, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8101, 32773, F8, 23) (dual of [32773, 32672, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8101, 32773, F8, 23) (dual of [32773, 32672, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8101, 32770, F8, 23) (dual of [32770, 32669, 24]-code), using
- net defined by OOA [i] based on linear OOA(8101, 2979, F8, 23, 23) (dual of [(2979, 23), 68416, 24]-NRT-code), using
- digital (3, 14, 24)-net over F8, using
(115−23, 115, 5958)-Net in Base 8 — Constructive
(92, 115, 5958)-net in base 8, using
- 81 times duplication [i] based on (91, 114, 5958)-net in base 8, using
- net defined by OOA [i] based on OOA(8114, 5958, S8, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(8114, 65539, S8, 23), using
- discarding factors based on OA(8114, 65540, S8, 23), using
- discarding parts of the base [i] based on linear OA(1685, 65540, F16, 23) (dual of [65540, 65455, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(1685, 65536, F16, 23) (dual of [65536, 65451, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(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(22) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(1685, 65540, F16, 23) (dual of [65540, 65455, 24]-code), using
- discarding factors based on OA(8114, 65540, S8, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(8114, 65539, S8, 23), using
- net defined by OOA [i] based on OOA(8114, 5958, S8, 23, 23), using
(115−23, 115, 68002)-Net over F8 — Digital
Digital (92, 115, 68002)-net over F8, using
(115−23, 115, large)-Net in Base 8 — Upper bound on s
There is no (92, 115, large)-net in base 8, because
- 21 times m-reduction [i] would yield (92, 94, large)-net in base 8, but