Best Known (61, 76, s)-Nets in Base 8
(61, 76, 4705)-Net over F8 — Constructive and digital
Digital (61, 76, 4705)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 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 (51, 66, 4681)-net over F8, using
- net defined by OOA [i] based on linear OOA(866, 4681, F8, 15, 15) (dual of [(4681, 15), 70149, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using
- net defined by OOA [i] based on linear OOA(866, 4681, F8, 15, 15) (dual of [(4681, 15), 70149, 16]-NRT-code), using
- digital (3, 10, 24)-net over F8, using
(61, 76, 9362)-Net in Base 8 — Constructive
(61, 76, 9362)-net in base 8, using
- base change [i] based on digital (42, 57, 9362)-net over F16, using
- net defined by OOA [i] based on linear OOA(1657, 9362, F16, 15, 15) (dual of [(9362, 15), 140373, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(1657, 65535, F16, 15) (dual of [65535, 65478, 16]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(1657, 65536, F16, 15) (dual of [65536, 65479, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(1657, 65535, F16, 15) (dual of [65535, 65478, 16]-code), using
- net defined by OOA [i] based on linear OOA(1657, 9362, F16, 15, 15) (dual of [(9362, 15), 140373, 16]-NRT-code), using
(61, 76, 69007)-Net over F8 — Digital
Digital (61, 76, 69007)-net over F8, using
(61, 76, large)-Net in Base 8 — Upper bound on s
There is no (61, 76, large)-net in base 8, because
- 13 times m-reduction [i] would yield (61, 63, large)-net in base 8, but