Best Known (209−30, 209, s)-Nets in Base 4
(209−30, 209, 17479)-Net over F4 — Constructive and digital
Digital (179, 209, 17479)-net over F4, using
- 43 times duplication [i] based on digital (176, 206, 17479)-net over F4, using
- net defined by OOA [i] based on linear OOA(4206, 17479, F4, 30, 30) (dual of [(17479, 30), 524164, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(4206, 262185, F4, 30) (dual of [262185, 261979, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4206, 262187, F4, 30) (dual of [262187, 261981, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4206, 262187, F4, 30) (dual of [262187, 261981, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(4206, 262185, F4, 30) (dual of [262185, 261979, 31]-code), using
- net defined by OOA [i] based on linear OOA(4206, 17479, F4, 30, 30) (dual of [(17479, 30), 524164, 31]-NRT-code), using
(209−30, 209, 131095)-Net over F4 — Digital
Digital (179, 209, 131095)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4209, 131095, F4, 2, 30) (dual of [(131095, 2), 261981, 31]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4207, 131094, F4, 2, 30) (dual of [(131094, 2), 261981, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4207, 262188, F4, 30) (dual of [262188, 261981, 31]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4206, 262187, F4, 30) (dual of [262187, 261981, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4206, 262187, F4, 30) (dual of [262187, 261981, 31]-code), using
- OOA 2-folding [i] based on linear OA(4207, 262188, F4, 30) (dual of [262188, 261981, 31]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4207, 131094, F4, 2, 30) (dual of [(131094, 2), 261981, 31]-NRT-code), using
(209−30, 209, large)-Net in Base 4 — Upper bound on s
There is no (179, 209, large)-net in base 4, because
- 28 times m-reduction [i] would yield (179, 181, large)-net in base 4, but