Best Known (166, 166+35, s)-Nets in Base 4
(166, 166+35, 1539)-Net over F4 — Constructive and digital
Digital (166, 201, 1539)-net over F4, using
- 6 times m-reduction [i] based on digital (166, 207, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 69, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 69, 513)-net over F64, using
(166, 166+35, 16451)-Net over F4 — Digital
Digital (166, 201, 16451)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4201, 16451, F4, 35) (dual of [16451, 16250, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(25) [i] based on
- linear OA(4183, 16384, F4, 35) (dual of [16384, 16201, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(418, 67, F4, 8) (dual of [67, 49, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 68, F4, 8) (dual of [68, 50, 9]-code), using
- construction X applied to Ce(34) ⊂ Ce(25) [i] based on
(166, 166+35, large)-Net in Base 4 — Upper bound on s
There is no (166, 201, large)-net in base 4, because
- 33 times m-reduction [i] would yield (166, 168, large)-net in base 4, but