Best Known (185−24, 185, s)-Nets in Base 4
(185−24, 185, 87384)-Net over F4 — Constructive and digital
Digital (161, 185, 87384)-net over F4, using
- net defined by OOA [i] based on linear OOA(4185, 87384, F4, 24, 24) (dual of [(87384, 24), 2097031, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4185, 1048608, F4, 24) (dual of [1048608, 1048423, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4185, 1048610, F4, 24) (dual of [1048610, 1048425, 25]-code), using
- 1 times truncation [i] based on linear OA(4186, 1048611, F4, 25) (dual of [1048611, 1048425, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(4186, 1048611, F4, 25) (dual of [1048611, 1048425, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4185, 1048610, F4, 24) (dual of [1048610, 1048425, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4185, 1048608, F4, 24) (dual of [1048608, 1048423, 25]-code), using
(185−24, 185, 510364)-Net over F4 — Digital
Digital (161, 185, 510364)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4185, 510364, F4, 2, 24) (dual of [(510364, 2), 1020543, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4185, 524305, F4, 2, 24) (dual of [(524305, 2), 1048425, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4185, 1048610, F4, 24) (dual of [1048610, 1048425, 25]-code), using
- 1 times truncation [i] based on linear OA(4186, 1048611, F4, 25) (dual of [1048611, 1048425, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(4186, 1048611, F4, 25) (dual of [1048611, 1048425, 26]-code), using
- OOA 2-folding [i] based on linear OA(4185, 1048610, F4, 24) (dual of [1048610, 1048425, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(4185, 524305, F4, 2, 24) (dual of [(524305, 2), 1048425, 25]-NRT-code), using
(185−24, 185, large)-Net in Base 4 — Upper bound on s
There is no (161, 185, large)-net in base 4, because
- 22 times m-reduction [i] would yield (161, 163, large)-net in base 4, but