Best Known (198, 198+29, s)-Nets in Base 4
(198, 198+29, 74908)-Net over F4 — Constructive and digital
Digital (198, 227, 74908)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 10)-net over F4, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- digital (182, 211, 74898)-net over F4, using
- net defined by OOA [i] based on linear OOA(4211, 74898, F4, 29, 29) (dual of [(74898, 29), 2171831, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4211, 1048573, F4, 29) (dual of [1048573, 1048362, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4211, 1048573, F4, 29) (dual of [1048573, 1048362, 30]-code), using
- net defined by OOA [i] based on linear OOA(4211, 74898, F4, 29, 29) (dual of [(74898, 29), 2171831, 30]-NRT-code), using
- digital (2, 16, 10)-net over F4, using
(198, 198+29, 524326)-Net over F4 — Digital
Digital (198, 227, 524326)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4227, 524326, F4, 2, 29) (dual of [(524326, 2), 1048425, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4227, 1048652, F4, 29) (dual of [1048652, 1048425, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4226, 1048651, F4, 29) (dual of [1048651, 1048425, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(415, 75, F4, 7) (dual of [75, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4226, 1048651, F4, 29) (dual of [1048651, 1048425, 30]-code), using
- OOA 2-folding [i] based on linear OA(4227, 1048652, F4, 29) (dual of [1048652, 1048425, 30]-code), using
(198, 198+29, large)-Net in Base 4 — Upper bound on s
There is no (198, 227, large)-net in base 4, because
- 27 times m-reduction [i] would yield (198, 200, large)-net in base 4, but