Best Known (150−18, 150, s)-Nets in Base 9
(150−18, 150, 1864162)-Net over F9 — Constructive and digital
Digital (132, 150, 1864162)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 12, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-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 (3, 12, 28)-net over F9, using
(150−18, 150, large)-Net over F9 — Digital
Digital (132, 150, large)-net over F9, using
- 95 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
(150−18, 150, large)-Net in Base 9 — Upper bound on s
There is no (132, 150, large)-net in base 9, because
- 16 times m-reduction [i] would yield (132, 134, large)-net in base 9, but