Best Known (242−18, 242, s)-Nets in Base 3
(242−18, 242, 1062903)-Net over F3 — Constructive and digital
Digital (224, 242, 1062903)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (9, 18, 21)-net over F3, using
- 3 times m-reduction [i] based on digital (9, 21, 21)-net over F3, using
- digital (206, 224, 1062882)-net over F3, using
- trace code for nets [i] based on 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
- trace code for nets [i] based on digital (94, 112, 531441)-net over F9, using
- digital (9, 18, 21)-net over F3, using
(242−18, 242, large)-Net over F3 — Digital
Digital (224, 242, large)-net over F3, using
- 31 times duplication [i] based on digital (223, 241, large)-net over F3, using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
(242−18, 242, large)-Net in Base 3 — Upper bound on s
There is no (224, 242, large)-net in base 3, because
- 16 times m-reduction [i] would yield (224, 226, large)-net in base 3, but