Best Known (120, 151, s)-Nets in Base 8
(120, 151, 2193)-Net over F8 — Constructive and digital
Digital (120, 151, 2193)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (105, 136, 2184)-net over F8, using
- net defined by OOA [i] based on linear OOA(8136, 2184, F8, 31, 31) (dual of [(2184, 31), 67568, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8136, 32761, F8, 31) (dual of [32761, 32625, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8136, 32761, F8, 31) (dual of [32761, 32625, 32]-code), using
- net defined by OOA [i] based on linear OOA(8136, 2184, F8, 31, 31) (dual of [(2184, 31), 67568, 32]-NRT-code), using
- digital (0, 15, 9)-net over F8, using
(120, 151, 60444)-Net over F8 — Digital
Digital (120, 151, 60444)-net over F8, using
(120, 151, large)-Net in Base 8 — Upper bound on s
There is no (120, 151, large)-net in base 8, because
- 29 times m-reduction [i] would yield (120, 122, large)-net in base 8, but