Best Known (183−20, 183, s)-Nets in Base 3
(183−20, 183, 478298)-Net over F3 — Constructive and digital
Digital (163, 183, 478298)-net over F3, using
- net defined by OOA [i] based on linear OOA(3183, 478298, F3, 20, 20) (dual of [(478298, 20), 9565777, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3183, 4782980, F3, 20) (dual of [4782980, 4782797, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3183, 4782983, F3, 20) (dual of [4782983, 4782800, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3183, 4782983, F3, 20) (dual of [4782983, 4782800, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3183, 4782980, F3, 20) (dual of [4782980, 4782797, 21]-code), using
(183−20, 183, 1195745)-Net over F3 — Digital
Digital (163, 183, 1195745)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3183, 1195745, F3, 4, 20) (dual of [(1195745, 4), 4782797, 21]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3183, 4782980, F3, 20) (dual of [4782980, 4782797, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3183, 4782983, F3, 20) (dual of [4782983, 4782800, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3183, 4782983, F3, 20) (dual of [4782983, 4782800, 21]-code), using
- OOA 4-folding [i] based on linear OA(3183, 4782980, F3, 20) (dual of [4782980, 4782797, 21]-code), using
(183−20, 183, large)-Net in Base 3 — Upper bound on s
There is no (163, 183, large)-net in base 3, because
- 18 times m-reduction [i] would yield (163, 165, large)-net in base 3, but