Best Known (160, 160+28, s)-Nets in Base 4
(160, 160+28, 4698)-Net over F4 — Constructive and digital
Digital (160, 188, 4698)-net over F4, using
- t-expansion [i] based on digital (159, 188, 4698)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (140, 169, 4681)-net over F4, using
- net defined by OOA [i] based on linear OOA(4169, 4681, F4, 29, 29) (dual of [(4681, 29), 135580, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4169, 65535, F4, 29) (dual of [65535, 65366, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4169, 65535, F4, 29) (dual of [65535, 65366, 30]-code), using
- net defined by OOA [i] based on linear OOA(4169, 4681, F4, 29, 29) (dual of [(4681, 29), 135580, 30]-NRT-code), using
- digital (5, 19, 17)-net over F4, using
- (u, u+v)-construction [i] based on
(160, 160+28, 65611)-Net over F4 — Digital
Digital (160, 188, 65611)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4188, 65611, F4, 28) (dual of [65611, 65423, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(18) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(419, 75, F4, 8) (dual of [75, 56, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(419, 87, F4, 8) (dual of [87, 68, 9]-code), using
- construction X applied to Ce(28) ⊂ Ce(18) [i] based on
(160, 160+28, large)-Net in Base 4 — Upper bound on s
There is no (160, 188, large)-net in base 4, because
- 26 times m-reduction [i] would yield (160, 162, large)-net in base 4, but