Best Known (157, 180, s)-Nets in Base 4
(157, 180, 95329)-Net over F4 — Constructive and digital
Digital (157, 180, 95329)-net over F4, using
- 41 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(4179, 95329, F4, 23, 23) (dual of [(95329, 23), 2192388, 24]-NRT-code), using
(157, 180, 524313)-Net over F4 — Digital
Digital (157, 180, 524313)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4180, 524313, F4, 2, 23) (dual of [(524313, 2), 1048446, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4180, 1048626, F4, 23) (dual of [1048626, 1048446, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 1048627, F4, 23) (dual of [1048627, 1048447, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [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(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(4180, 1048627, F4, 23) (dual of [1048627, 1048447, 24]-code), using
- OOA 2-folding [i] based on linear OA(4180, 1048626, F4, 23) (dual of [1048626, 1048446, 24]-code), using
(157, 180, large)-Net in Base 4 — Upper bound on s
There is no (157, 180, large)-net in base 4, because
- 21 times m-reduction [i] would yield (157, 159, large)-net in base 4, but