Best Known (202, 218, s)-Nets in Base 3
(202, 218, 1447159)-Net over F3 — Constructive and digital
Digital (202, 218, 1447159)-net over F3, using
- 31 times duplication [i] based on digital (201, 217, 1447159)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (58, 66, 398584)-net over F3, using
- net defined by OOA [i] based on linear OOA(366, 398584, F3, 8, 8) (dual of [(398584, 8), 3188606, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(366, 1594336, F3, 8) (dual of [1594336, 1594270, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(366, 1594323, F3, 8) (dual of [1594323, 1594257, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(353, 1594323, F3, 7) (dual of [1594323, 1594270, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 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
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(366, 1594336, F3, 8) (dual of [1594336, 1594270, 9]-code), using
- net defined by OOA [i] based on linear OOA(366, 398584, F3, 8, 8) (dual of [(398584, 8), 3188606, 9]-NRT-code), using
- digital (135, 151, 1048575)-net over F3, using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- digital (58, 66, 398584)-net over F3, using
- (u, u+v)-construction [i] based on
(202, 218, large)-Net over F3 — Digital
Digital (202, 218, large)-net over F3, using
- 32 times duplication [i] based on digital (200, 216, large)-net over F3, using
- t-expansion [i] based on digital (198, 216, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3216, large, F3, 18) (dual of [large, large−216, 19]-code), using
- 36 times code embedding in larger space [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 36 times code embedding in larger space [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3216, large, F3, 18) (dual of [large, large−216, 19]-code), using
- t-expansion [i] based on digital (198, 216, large)-net over F3, using
(202, 218, large)-Net in Base 3 — Upper bound on s
There is no (202, 218, large)-net in base 3, because
- 14 times m-reduction [i] would yield (202, 204, large)-net in base 3, but