Best Known (117, 117+29, s)-Nets in Base 8
(117, 117+29, 2369)-Net over F8 — Constructive and digital
Digital (117, 146, 2369)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 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 (98, 127, 2341)-net over F8, using
- net defined by OOA [i] based on linear OOA(8127, 2341, F8, 29, 29) (dual of [(2341, 29), 67762, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8127, 32775, F8, 29) (dual of [32775, 32648, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8127, 32779, F8, 29) (dual of [32779, 32652, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(8127, 32779, F8, 29) (dual of [32779, 32652, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8127, 32775, F8, 29) (dual of [32775, 32648, 30]-code), using
- net defined by OOA [i] based on linear OOA(8127, 2341, F8, 29, 29) (dual of [(2341, 29), 67762, 30]-NRT-code), using
- digital (5, 19, 28)-net over F8, using
(117, 117+29, 4681)-Net in Base 8 — Constructive
(117, 146, 4681)-net in base 8, using
- net defined by OOA [i] based on OOA(8146, 4681, S8, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(8146, 65535, S8, 29), using
- discarding factors based on OA(8146, 65540, S8, 29), using
- discarding parts of the base [i] based on linear OA(16109, 65540, F16, 29) (dual of [65540, 65431, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(28) ⊂ Ce(27) [i] based on
- discarding parts of the base [i] based on linear OA(16109, 65540, F16, 29) (dual of [65540, 65431, 30]-code), using
- discarding factors based on OA(8146, 65540, S8, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(8146, 65535, S8, 29), using
(117, 117+29, 82594)-Net over F8 — Digital
Digital (117, 146, 82594)-net over F8, using
(117, 117+29, large)-Net in Base 8 — Upper bound on s
There is no (117, 146, large)-net in base 8, because
- 27 times m-reduction [i] would yield (117, 119, large)-net in base 8, but