Best Known (184, 184+16, s)-Nets in Base 3
(184, 184+16, 1195746)-Net over F3 — Constructive and digital
Digital (184, 200, 1195746)-net over F3, using
- trace code for nets [i] based on digital (84, 100, 597873)-net over F9, using
- net defined by OOA [i] based on linear OOA(9100, 597873, F9, 16, 16) (dual of [(597873, 16), 9565868, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(9100, 4782984, F9, 16) (dual of [4782984, 4782884, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(91, 15, F9, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- OA 8-folding and stacking [i] based on linear OA(9100, 4782984, F9, 16) (dual of [4782984, 4782884, 17]-code), using
- net defined by OOA [i] based on linear OOA(9100, 597873, F9, 16, 16) (dual of [(597873, 16), 9565868, 17]-NRT-code), using
(184, 184+16, large)-Net over F3 — Digital
Digital (184, 200, large)-net over F3, using
- 39 times duplication [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
(184, 184+16, large)-Net in Base 3 — Upper bound on s
There is no (184, 200, large)-net in base 3, because
- 14 times m-reduction [i] would yield (184, 186, large)-net in base 3, but