Best Known (215−31, 215, s)-Nets in Base 4
(215−31, 215, 17479)-Net over F4 — Constructive and digital
Digital (184, 215, 17479)-net over F4, using
- net defined by OOA [i] based on linear OOA(4215, 17479, F4, 31, 31) (dual of [(17479, 31), 541634, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(4215, 262186, F4, 31) (dual of [262186, 261971, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(4215, 262187, F4, 31) (dual of [262187, 261972, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(4208, 262144, F4, 31) (dual of [262144, 261936, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4215, 262187, F4, 31) (dual of [262187, 261972, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(4215, 262186, F4, 31) (dual of [262186, 261971, 32]-code), using
(215−31, 215, 131093)-Net over F4 — Digital
Digital (184, 215, 131093)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4215, 131093, F4, 2, 31) (dual of [(131093, 2), 261971, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4215, 262186, F4, 31) (dual of [262186, 261971, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(4215, 262187, F4, 31) (dual of [262187, 261972, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(4208, 262144, F4, 31) (dual of [262144, 261936, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4215, 262187, F4, 31) (dual of [262187, 261972, 32]-code), using
- OOA 2-folding [i] based on linear OA(4215, 262186, F4, 31) (dual of [262186, 261971, 32]-code), using
(215−31, 215, large)-Net in Base 4 — Upper bound on s
There is no (184, 215, large)-net in base 4, because
- 29 times m-reduction [i] would yield (184, 186, large)-net in base 4, but