Best Known (179−23, 179, s)-Nets in Base 4
(179−23, 179, 95329)-Net over F4 — Constructive and digital
Digital (156, 179, 95329)-net over F4, using
- net defined by OOA [i] based on linear OOA(4179, 95329, F4, 23, 23) (dual of [(95329, 23), 2192388, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4179, 1048620, F4, 23) (dual of [1048620, 1048441, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4179, 1048624, F4, 23) (dual of [1048624, 1048445, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4179, 1048624, F4, 23) (dual of [1048624, 1048445, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4179, 1048620, F4, 23) (dual of [1048620, 1048441, 24]-code), using
(179−23, 179, 524312)-Net over F4 — Digital
Digital (156, 179, 524312)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4179, 524312, F4, 2, 23) (dual of [(524312, 2), 1048445, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4179, 1048624, F4, 23) (dual of [1048624, 1048445, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(4179, 1048624, F4, 23) (dual of [1048624, 1048445, 24]-code), using
(179−23, 179, large)-Net in Base 4 — Upper bound on s
There is no (156, 179, large)-net in base 4, because
- 21 times m-reduction [i] would yield (156, 158, large)-net in base 4, but