Best Known (66, 83, s)-Nets in Base 8
(66, 83, 4121)-Net over F8 — Constructive and digital
Digital (66, 83, 4121)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-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 (4, 12, 25)-net over F8, using
(66, 83, 8192)-Net in Base 8 — Constructive
(66, 83, 8192)-net in base 8, using
- net defined by OOA [i] based on OOA(883, 8192, S8, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(883, 65537, S8, 17), using
- discarding factors based on OA(883, 65541, S8, 17), using
- discarding parts of the base [i] based on linear OA(1662, 65541, F16, 17) (dual of [65541, 65479, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [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(1657, 65536, F16, 15) (dual of [65536, 65479, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(161, 5, F16, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(1662, 65541, F16, 17) (dual of [65541, 65479, 18]-code), using
- discarding factors based on OA(883, 65541, S8, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(883, 65537, S8, 17), using
(66, 83, 47021)-Net over F8 — Digital
Digital (66, 83, 47021)-net over F8, using
(66, 83, large)-Net in Base 8 — Upper bound on s
There is no (66, 83, large)-net in base 8, because
- 15 times m-reduction [i] would yield (66, 68, large)-net in base 8, but