Best Known (184, 184+21, s)-Nets in Base 3
(184, 184+21, 478301)-Net over F3 — Constructive and digital
Digital (184, 205, 478301)-net over F3, using
- 32 times duplication [i] based on digital (182, 203, 478301)-net over F3, using
- net defined by OOA [i] based on linear OOA(3203, 478301, F3, 21, 21) (dual of [(478301, 21), 10044118, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3203, 4783011, F3, 21) (dual of [4783011, 4782808, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3203, 4783017, F3, 21) (dual of [4783017, 4782814, 22]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3203, 4783017, F3, 21) (dual of [4783017, 4782814, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3203, 4783011, F3, 21) (dual of [4783011, 4782808, 22]-code), using
- net defined by OOA [i] based on linear OOA(3203, 478301, F3, 21, 21) (dual of [(478301, 21), 10044118, 22]-NRT-code), using
(184, 184+21, 1594339)-Net over F3 — Digital
Digital (184, 205, 1594339)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3205, 1594339, F3, 3, 21) (dual of [(1594339, 3), 4782812, 22]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3206, 1594340, F3, 3, 22) (dual of [(1594340, 3), 4782814, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3206, 4783020, F3, 22) (dual of [4783020, 4782814, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(39, 51, F3, 4) (dual of [51, 42, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OOA 3-folding [i] based on linear OA(3206, 4783020, F3, 22) (dual of [4783020, 4782814, 23]-code), using
- 1 step truncation [i] based on linear OOA(3206, 1594340, F3, 3, 22) (dual of [(1594340, 3), 4782814, 23]-NRT-code), using
(184, 184+21, large)-Net in Base 3 — Upper bound on s
There is no (184, 205, large)-net in base 3, because
- 19 times m-reduction [i] would yield (184, 186, large)-net in base 3, but