Best Known (223, 245, s)-Nets in Base 3
(223, 245, 762684)-Net over F3 — Constructive and digital
Digital (223, 245, 762684)-net over F3, using
- 31 times duplication [i] based on 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
- (u, u+v)-construction [i] based on
(223, 245, 4194411)-Net over F3 — Digital
Digital (223, 245, 4194411)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3245, 4194411, F3, 2, 22) (dual of [(4194411, 2), 8388577, 23]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(334, 110, F3, 2, 11) (dual of [(110, 2), 186, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(334, 110, F3, 11) (dual of [110, 76, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(334, 115, F3, 11) (dual of [115, 81, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(333, 113, F3, 11) (dual of [113, 80, 12]-code), using
- a “BZ†code from Brouwer’s database [i]
- linear OA(333, 114, F3, 10) (dual of [114, 81, 11]-code), using Gilbert–Varšamov bound and bm = 333 > Vbs−1(k−1) = 3192 777628 940355 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(333, 113, F3, 11) (dual of [113, 80, 12]-code), using
- construction X with Varšamov bound [i] based on
- discarding factors / shortening the dual code based on linear OA(334, 115, F3, 11) (dual of [115, 81, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(334, 110, F3, 11) (dual of [110, 76, 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(334, 110, F3, 2, 11) (dual of [(110, 2), 186, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
(223, 245, large)-Net in Base 3 — Upper bound on s
There is no (223, 245, large)-net in base 3, because
- 20 times m-reduction [i] would yield (223, 225, large)-net in base 3, but