Best Known (161−17, 161, s)-Nets in Base 3
(161−17, 161, 597877)-Net over F3 — Constructive and digital
Digital (144, 161, 597877)-net over F3, using
- net defined by OOA [i] based on linear OOA(3161, 597877, F3, 17, 17) (dual of [(597877, 17), 10163748, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3161, 4783017, F3, 17) (dual of [4783017, 4782856, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- 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(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(3161, 4783017, F3, 17) (dual of [4783017, 4782856, 18]-code), using
(161−17, 161, 1594339)-Net over F3 — Digital
Digital (144, 161, 1594339)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3161, 1594339, F3, 3, 17) (dual of [(1594339, 3), 4782856, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3161, 4783017, F3, 17) (dual of [4783017, 4782856, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- 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(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- OOA 3-folding [i] based on linear OA(3161, 4783017, F3, 17) (dual of [4783017, 4782856, 18]-code), using
(161−17, 161, large)-Net in Base 3 — Upper bound on s
There is no (144, 161, large)-net in base 3, because
- 15 times m-reduction [i] would yield (144, 146, large)-net in base 3, but