Best Known (84−17, 84, s)-Nets in Base 8
(84−17, 84, 4124)-Net over F8 — Constructive and digital
Digital (67, 84, 4124)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 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 (54, 71, 4096)-net over F8, using
- net defined by OOA [i] based on linear OOA(871, 4096, F8, 17, 17) (dual of [(4096, 17), 69561, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- net defined by OOA [i] based on linear OOA(871, 4096, F8, 17, 17) (dual of [(4096, 17), 69561, 18]-NRT-code), using
- digital (5, 13, 28)-net over F8, using
(84−17, 84, 8193)-Net in Base 8 — Constructive
(67, 84, 8193)-net in base 8, using
- base change [i] based on digital (46, 63, 8193)-net over F16, using
- net defined by OOA [i] based on linear OOA(1663, 8193, F16, 17, 17) (dual of [(8193, 17), 139218, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1663, 65545, F16, 17) (dual of [65545, 65482, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1663, 65546, F16, 17) (dual of [65546, 65483, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- 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(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(162, 10, F16, 2) (dual of [10, 8, 3]-code or 10-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(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(1663, 65546, F16, 17) (dual of [65546, 65483, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1663, 65545, F16, 17) (dual of [65545, 65482, 18]-code), using
- net defined by OOA [i] based on linear OOA(1663, 8193, F16, 17, 17) (dual of [(8193, 17), 139218, 18]-NRT-code), using
(84−17, 84, 53546)-Net over F8 — Digital
Digital (67, 84, 53546)-net over F8, using
(84−17, 84, large)-Net in Base 8 — Upper bound on s
There is no (67, 84, large)-net in base 8, because
- 15 times m-reduction [i] would yield (67, 69, large)-net in base 8, but