Best Known (154, 177, s)-Nets in Base 4
(154, 177, 95328)-Net over F4 — Constructive and digital
Digital (154, 177, 95328)-net over F4, using
- 41 times duplication [i] based on digital (153, 176, 95328)-net over F4, using
- net defined by OOA [i] based on linear OOA(4176, 95328, F4, 23, 23) (dual of [(95328, 23), 2192368, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4176, 1048609, F4, 23) (dual of [1048609, 1048433, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4176, 1048611, F4, 23) (dual of [1048611, 1048435, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [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(4141, 1048576, F4, 19) (dual of [1048576, 1048435, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4176, 1048611, F4, 23) (dual of [1048611, 1048435, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4176, 1048609, F4, 23) (dual of [1048609, 1048433, 24]-code), using
- net defined by OOA [i] based on linear OOA(4176, 95328, F4, 23, 23) (dual of [(95328, 23), 2192368, 24]-NRT-code), using
(154, 177, 513094)-Net over F4 — Digital
Digital (154, 177, 513094)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4177, 513094, F4, 2, 23) (dual of [(513094, 2), 1026011, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4177, 524306, F4, 2, 23) (dual of [(524306, 2), 1048435, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4177, 1048612, F4, 23) (dual of [1048612, 1048435, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4176, 1048611, F4, 23) (dual of [1048611, 1048435, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [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(4141, 1048576, F4, 19) (dual of [1048576, 1048435, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(22) ⊂ Ce(18) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4176, 1048611, F4, 23) (dual of [1048611, 1048435, 24]-code), using
- OOA 2-folding [i] based on linear OA(4177, 1048612, F4, 23) (dual of [1048612, 1048435, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(4177, 524306, F4, 2, 23) (dual of [(524306, 2), 1048435, 24]-NRT-code), using
(154, 177, large)-Net in Base 4 — Upper bound on s
There is no (154, 177, large)-net in base 4, because
- 21 times m-reduction [i] would yield (154, 156, large)-net in base 4, but