Best Known (185−23, 185, s)-Nets in Base 4
(185−23, 185, 95339)-Net over F4 — Constructive and digital
Digital (162, 185, 95339)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (148, 171, 95325)-net over F4, using
- net defined by OOA [i] based on linear OOA(4171, 95325, F4, 23, 23) (dual of [(95325, 23), 2192304, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [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]
- OOA 11-folding and stacking with additional row [i] based on linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using
- net defined by OOA [i] based on linear OOA(4171, 95325, F4, 23, 23) (dual of [(95325, 23), 2192304, 24]-NRT-code), using
- digital (3, 14, 14)-net over F4, using
(185−23, 185, 545193)-Net over F4 — Digital
Digital (162, 185, 545193)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4185, 545193, F4, 23) (dual of [545193, 545008, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4185, 1048640, F4, 23) (dual of [1048640, 1048455, 24]-code), using
- 4 times code embedding in larger space [i] based on linear OA(4181, 1048636, F4, 23) (dual of [1048636, 1048455, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [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(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- 4 times code embedding in larger space [i] based on linear OA(4181, 1048636, F4, 23) (dual of [1048636, 1048455, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4185, 1048640, F4, 23) (dual of [1048640, 1048455, 24]-code), using
(185−23, 185, large)-Net in Base 4 — Upper bound on s
There is no (162, 185, large)-net in base 4, because
- 21 times m-reduction [i] would yield (162, 164, large)-net in base 4, but