Best Known (222, 244, s)-Nets in Base 3
(222, 244, 762684)-Net over F3 — Constructive and digital
Digital (222, 244, 762684)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (22, 33, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 11, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 11, 28)-net over F27, using
- digital (189, 211, 762600)-net over F3, using
- net defined by OOA [i] based on linear OOA(3211, 762600, F3, 22, 22) (dual of [(762600, 22), 16776989, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3211, 8388600, F3, 22) (dual of [8388600, 8388389, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3211, 8388600, F3, 22) (dual of [8388600, 8388389, 23]-code), using
- net defined by OOA [i] based on linear OOA(3211, 762600, F3, 22, 22) (dual of [(762600, 22), 16776989, 23]-NRT-code), using
- digital (22, 33, 84)-net over F3, using
(222, 244, 4194397)-Net over F3 — Digital
Digital (222, 244, 4194397)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3244, 4194397, F3, 2, 22) (dual of [(4194397, 2), 8388550, 23]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(333, 96, F3, 2, 11) (dual of [(96, 2), 159, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(333, 96, F3, 11) (dual of [96, 63, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(333, 97, F3, 11) (dual of [97, 64, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(332, 96, F3, 11) (dual of [96, 64, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(327, 81, F3, 11) (dual of [81, 54, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(317, 81, F3, 7) (dual of [81, 64, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(35, 15, F3, 3) (dual of [15, 10, 4]-code or 15-cap in PG(4,3)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(332, 96, F3, 11) (dual of [96, 64, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(333, 97, F3, 11) (dual of [97, 64, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(333, 96, F3, 11) (dual of [96, 63, 12]-code), using
- linear OOA(3211, 4194301, F3, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- linear OOA(333, 96, F3, 2, 11) (dual of [(96, 2), 159, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
(222, 244, large)-Net in Base 3 — Upper bound on s
There is no (222, 244, large)-net in base 3, because
- 20 times m-reduction [i] would yield (222, 224, large)-net in base 3, but