Best Known (109, 109+18, s)-Nets in Base 9
(109, 109+18, 531475)-Net over F9 — Constructive and digital
Digital (109, 127, 531475)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 15, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (94, 112, 531441)-net over F9, using
- net defined by OOA [i] based on linear OOA(9112, 531441, F9, 18, 18) (dual of [(531441, 18), 9565826, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- net defined by OOA [i] based on linear OOA(9112, 531441, F9, 18, 18) (dual of [(531441, 18), 9565826, 19]-NRT-code), using
- digital (6, 15, 34)-net over F9, using
(109, 109+18, 531479)-Net in Base 9 — Constructive
(109, 127, 531479)-net in base 9, using
- (u, u+v)-construction [i] based on
- (6, 15, 38)-net in base 9, using
- base change [i] based on digital (1, 10, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- base change [i] based on digital (1, 10, 38)-net over F27, using
- digital (94, 112, 531441)-net over F9, using
- net defined by OOA [i] based on linear OOA(9112, 531441, F9, 18, 18) (dual of [(531441, 18), 9565826, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- net defined by OOA [i] based on linear OOA(9112, 531441, F9, 18, 18) (dual of [(531441, 18), 9565826, 19]-NRT-code), using
- (6, 15, 38)-net in base 9, using
(109, 109+18, large)-Net over F9 — Digital
Digital (109, 127, large)-net over F9, using
- 92 times duplication [i] based on digital (107, 125, large)-net over F9, using
(109, 109+18, large)-Net in Base 9 — Upper bound on s
There is no (109, 127, large)-net in base 9, because
- 16 times m-reduction [i] would yield (109, 111, large)-net in base 9, but