Best Known (180, 194, s)-Nets in Base 3
(180, 194, 2396742)-Net over F3 — Constructive and digital
Digital (180, 194, 2396742)-net over F3, using
- trace code for nets [i] based on digital (83, 97, 1198371)-net over F9, using
- net defined by OOA [i] based on linear OOA(997, 1198371, F9, 14, 14) (dual of [(1198371, 14), 16777097, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(997, 8388597, F9, 14) (dual of [8388597, 8388500, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(997, large, F9, 14) (dual of [large, large−97, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(997, large, F9, 14) (dual of [large, large−97, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(997, 8388597, F9, 14) (dual of [8388597, 8388500, 15]-code), using
- net defined by OOA [i] based on linear OOA(997, 1198371, F9, 14, 14) (dual of [(1198371, 14), 16777097, 15]-NRT-code), using
(180, 194, large)-Net over F3 — Digital
Digital (180, 194, large)-net over F3, using
- 33 times duplication [i] based on digital (177, 191, large)-net over F3, using
- t-expansion [i] based on digital (175, 191, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3191, large, F3, 16) (dual of [large, large−191, 17]-code), using
- 40 times code embedding in larger space [i] 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]
- 40 times code embedding in larger space [i] based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3191, large, F3, 16) (dual of [large, large−191, 17]-code), using
- t-expansion [i] based on digital (175, 191, large)-net over F3, using
(180, 194, large)-Net in Base 3 — Upper bound on s
There is no (180, 194, large)-net in base 3, because
- 12 times m-reduction [i] would yield (180, 182, large)-net in base 3, but