Best Known (178, 206, s)-Nets in Base 4
(178, 206, 18738)-Net over F4 — Constructive and digital
Digital (178, 206, 18738)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 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 (161, 189, 18724)-net over F4, using
- net defined by OOA [i] based on linear OOA(4189, 18724, F4, 28, 28) (dual of [(18724, 28), 524083, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4189, 262136, F4, 28) (dual of [262136, 261947, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4189, 262143, F4, 28) (dual of [262143, 261954, 29]-code), using
- 1 times truncation [i] based on linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 1 times truncation [i] based on linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4189, 262143, F4, 28) (dual of [262143, 261954, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(4189, 262136, F4, 28) (dual of [262136, 261947, 29]-code), using
- net defined by OOA [i] based on linear OOA(4189, 18724, F4, 28, 28) (dual of [(18724, 28), 524083, 29]-NRT-code), using
- digital (3, 17, 14)-net over F4, using
(178, 206, 196398)-Net over F4 — Digital
Digital (178, 206, 196398)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4206, 196398, F4, 28) (dual of [196398, 196192, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4206, 262214, F4, 28) (dual of [262214, 262008, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(416, 70, F4, 6) (dual of [70, 54, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 85, F4, 6) (dual of [85, 69, 7]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4206, 262214, F4, 28) (dual of [262214, 262008, 29]-code), using
(178, 206, large)-Net in Base 4 — Upper bound on s
There is no (178, 206, large)-net in base 4, because
- 26 times m-reduction [i] would yield (178, 180, large)-net in base 4, but