Best Known (147−18, 147, s)-Nets in Base 9
(147−18, 147, 1864144)-Net over F9 — Constructive and digital
Digital (129, 147, 1864144)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (120, 138, 1864134)-net over F9, using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F81, using
- net defined by OOA [i] based on linear OOA(8169, 932067, F81, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8169, large, F81, 18) (dual of [large, large−69, 19]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(8169, large, F81, 18) (dual of [large, large−69, 19]-code), using
- net defined by OOA [i] based on linear OOA(8169, 932067, F81, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F81, using
- digital (0, 9, 10)-net over F9, using
(147−18, 147, large)-Net over F9 — Digital
Digital (129, 147, large)-net over F9, using
- 92 times duplication [i] based on digital (127, 145, large)-net over F9, using
- t-expansion [i] based on digital (124, 145, large)-net over F9, using
(147−18, 147, large)-Net in Base 9 — Upper bound on s
There is no (129, 147, large)-net in base 9, because
- 16 times m-reduction [i] would yield (129, 131, large)-net in base 9, but