Best Known (218−22, 218, s)-Nets in Base 3
(218−22, 218, 762600)-Net over F3 — Constructive and digital
Digital (196, 218, 762600)-net over F3, using
- 37 times duplication [i] based on 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
(218−22, 218, 2097152)-Net over F3 — Digital
Digital (196, 218, 2097152)-net over F3, using
- 31 times duplication [i] based on digital (195, 217, 2097152)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3217, 2097152, F3, 4, 22) (dual of [(2097152, 4), 8388391, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3213, 2097151, F3, 4, 22) (dual of [(2097151, 4), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3213, 4194302, F3, 2, 22) (dual of [(4194302, 2), 8388391, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on 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
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3211, 4194301, F3, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3213, 4194302, F3, 2, 22) (dual of [(4194302, 2), 8388391, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3213, 2097151, F3, 4, 22) (dual of [(2097151, 4), 8388391, 23]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3217, 2097152, F3, 4, 22) (dual of [(2097152, 4), 8388391, 23]-NRT-code), using
(218−22, 218, large)-Net in Base 3 — Upper bound on s
There is no (196, 218, large)-net in base 3, because
- 20 times m-reduction [i] would yield (196, 198, large)-net in base 3, but