Best Known (171, 197, s)-Nets in Base 4
(171, 197, 80662)-Net over F4 — Constructive and digital
Digital (171, 197, 80662)-net over F4, using
- 41 times duplication [i] based on digital (170, 196, 80662)-net over F4, using
- net defined by OOA [i] based on linear OOA(4196, 80662, F4, 26, 26) (dual of [(80662, 26), 2097016, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4196, 1048606, F4, 26) (dual of [1048606, 1048410, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4196, 1048611, F4, 26) (dual of [1048611, 1048415, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(4191, 1048576, F4, 26) (dual of [1048576, 1048385, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4196, 1048611, F4, 26) (dual of [1048611, 1048415, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4196, 1048606, F4, 26) (dual of [1048606, 1048410, 27]-code), using
- net defined by OOA [i] based on linear OOA(4196, 80662, F4, 26, 26) (dual of [(80662, 26), 2097016, 27]-NRT-code), using
(171, 197, 399703)-Net over F4 — Digital
Digital (171, 197, 399703)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4197, 399703, F4, 2, 26) (dual of [(399703, 2), 799209, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4197, 524306, F4, 2, 26) (dual of [(524306, 2), 1048415, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4197, 1048612, F4, 26) (dual of [1048612, 1048415, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4196, 1048611, F4, 26) (dual of [1048611, 1048415, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(4191, 1048576, F4, 26) (dual of [1048576, 1048385, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4196, 1048611, F4, 26) (dual of [1048611, 1048415, 27]-code), using
- OOA 2-folding [i] based on linear OA(4197, 1048612, F4, 26) (dual of [1048612, 1048415, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(4197, 524306, F4, 2, 26) (dual of [(524306, 2), 1048415, 27]-NRT-code), using
(171, 197, large)-Net in Base 4 — Upper bound on s
There is no (171, 197, large)-net in base 4, because
- 24 times m-reduction [i] would yield (171, 173, large)-net in base 4, but