Best Known (173−23, 173, s)-Nets in Base 4
(173−23, 173, 95327)-Net over F4 — Constructive and digital
Digital (150, 173, 95327)-net over F4, using
- net defined by OOA [i] based on linear OOA(4173, 95327, F4, 23, 23) (dual of [(95327, 23), 2192348, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4173, 1048598, F4, 23) (dual of [1048598, 1048425, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4172, 1048597, F4, 23) (dual of [1048597, 1048425, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [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(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(41, 21, F4, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4172, 1048597, F4, 23) (dual of [1048597, 1048425, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4173, 1048598, F4, 23) (dual of [1048598, 1048425, 24]-code), using
(173−23, 173, 388848)-Net over F4 — Digital
Digital (150, 173, 388848)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4173, 388848, F4, 2, 23) (dual of [(388848, 2), 777523, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4173, 524299, F4, 2, 23) (dual of [(524299, 2), 1048425, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4173, 1048598, F4, 23) (dual of [1048598, 1048425, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4172, 1048597, F4, 23) (dual of [1048597, 1048425, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [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(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(41, 21, F4, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4172, 1048597, F4, 23) (dual of [1048597, 1048425, 24]-code), using
- OOA 2-folding [i] based on linear OA(4173, 1048598, F4, 23) (dual of [1048598, 1048425, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(4173, 524299, F4, 2, 23) (dual of [(524299, 2), 1048425, 24]-NRT-code), using
(173−23, 173, large)-Net in Base 4 — Upper bound on s
There is no (150, 173, large)-net in base 4, because
- 21 times m-reduction [i] would yield (150, 152, large)-net in base 4, but