Best Known (26, 31, s)-Nets in Base 4
(26, 31, 524287)-Net over F4 — Constructive and digital
Digital (26, 31, 524287)-net over F4, using
- net defined by OOA [i] based on linear OOA(431, 524287, F4, 5, 5) (dual of [(524287, 5), 2621404, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(431, 1048575, F4, 5) (dual of [1048575, 1048544, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(431, 1048575, F4, 5) (dual of [1048575, 1048544, 6]-code), using
(26, 31, 635128)-Net over F4 — Digital
Digital (26, 31, 635128)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(431, 635128, F4, 5) (dual of [635128, 635097, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using
(26, 31, large)-Net in Base 4 — Upper bound on s
There is no (26, 31, large)-net in base 4, because
- 3 times m-reduction [i] would yield (26, 28, large)-net in base 4, but