Best Known (143, 166, s)-Nets in Base 4
(143, 166, 23841)-Net over F4 — Constructive and digital
Digital (143, 166, 23841)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (131, 154, 23832)-net over F4, using
- net defined by OOA [i] based on linear OOA(4154, 23832, F4, 23, 23) (dual of [(23832, 23), 547982, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4154, 262153, F4, 23) (dual of [262153, 261999, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4145, 262144, F4, 22) (dual of [262144, 261999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(4154, 262153, F4, 23) (dual of [262153, 261999, 24]-code), using
- net defined by OOA [i] based on linear OOA(4154, 23832, F4, 23, 23) (dual of [(23832, 23), 547982, 24]-NRT-code), using
- digital (1, 12, 9)-net over F4, using
(143, 166, 155524)-Net over F4 — Digital
Digital (143, 166, 155524)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4166, 155524, F4, 23) (dual of [155524, 155358, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 262201, F4, 23) (dual of [262201, 262035, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4164, 262199, F4, 23) (dual of [262199, 262035, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(410, 55, F4, 5) (dual of [55, 45, 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
- 2 times code embedding in larger space [i] based on linear OA(4164, 262199, F4, 23) (dual of [262199, 262035, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 262201, F4, 23) (dual of [262201, 262035, 24]-code), using
(143, 166, large)-Net in Base 4 — Upper bound on s
There is no (143, 166, large)-net in base 4, because
- 21 times m-reduction [i] would yield (143, 145, large)-net in base 4, but