Best Known (150−20, 150, s)-Nets in Base 4
(150−20, 150, 104857)-Net over F4 — Constructive and digital
Digital (130, 150, 104857)-net over F4, using
- net defined by OOA [i] based on linear OOA(4150, 104857, F4, 20, 20) (dual of [(104857, 20), 2096990, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4150, 1048570, F4, 20) (dual of [1048570, 1048420, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4150, 1048575, F4, 20) (dual of [1048575, 1048425, 21]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4150, 1048575, F4, 20) (dual of [1048575, 1048425, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(4150, 1048570, F4, 20) (dual of [1048570, 1048420, 21]-code), using
(150−20, 150, 417132)-Net over F4 — Digital
Digital (130, 150, 417132)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4150, 417132, F4, 2, 20) (dual of [(417132, 2), 834114, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4150, 524287, F4, 2, 20) (dual of [(524287, 2), 1048424, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4150, 1048574, F4, 20) (dual of [1048574, 1048424, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4150, 1048575, F4, 20) (dual of [1048575, 1048425, 21]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4150, 1048575, F4, 20) (dual of [1048575, 1048425, 21]-code), using
- OOA 2-folding [i] based on linear OA(4150, 1048574, F4, 20) (dual of [1048574, 1048424, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(4150, 524287, F4, 2, 20) (dual of [(524287, 2), 1048424, 21]-NRT-code), using
(150−20, 150, large)-Net in Base 4 — Upper bound on s
There is no (130, 150, large)-net in base 4, because
- 18 times m-reduction [i] would yield (130, 132, large)-net in base 4, but