Best Known (200−35, 200, s)-Nets in Base 4
(200−35, 200, 1539)-Net over F4 — Constructive and digital
Digital (165, 200, 1539)-net over F4, using
- t-expansion [i] based on digital (164, 200, 1539)-net over F4, using
- 4 times m-reduction [i] based on digital (164, 204, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 68, 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, 68, 513)-net over F64, using
- 4 times m-reduction [i] based on digital (164, 204, 1539)-net over F4, using
(200−35, 200, 16447)-Net over F4 — Digital
Digital (165, 200, 16447)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4200, 16447, F4, 35) (dual of [16447, 16247, 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(417, 63, F4, 8) (dual of [63, 46, 9]-code), using
- construction X applied to Ce(34) ⊂ Ce(25) [i] based on
(200−35, 200, large)-Net in Base 4 — Upper bound on s
There is no (165, 200, large)-net in base 4, because
- 33 times m-reduction [i] would yield (165, 167, large)-net in base 4, but