Best Known (149, 149+28, s)-Nets in Base 4
(149, 149+28, 4684)-Net over F4 — Constructive and digital
Digital (149, 177, 4684)-net over F4, using
- net defined by OOA [i] based on linear OOA(4177, 4684, F4, 28, 28) (dual of [(4684, 28), 130975, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4177, 65576, F4, 28) (dual of [65576, 65399, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4176, 65575, F4, 28) (dual of [65575, 65399, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4176, 65575, F4, 28) (dual of [65575, 65399, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(4177, 65576, F4, 28) (dual of [65576, 65399, 29]-code), using
(149, 149+28, 41825)-Net over F4 — Digital
Digital (149, 177, 41825)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4177, 41825, F4, 28) (dual of [41825, 41648, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4177, 65576, F4, 28) (dual of [65576, 65399, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4176, 65575, F4, 28) (dual of [65575, 65399, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4176, 65575, F4, 28) (dual of [65575, 65399, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4177, 65576, F4, 28) (dual of [65576, 65399, 29]-code), using
(149, 149+28, large)-Net in Base 4 — Upper bound on s
There is no (149, 177, large)-net in base 4, because
- 26 times m-reduction [i] would yield (149, 151, large)-net in base 4, but