Best Known (159, 159+34, s)-Nets in Base 4
(159, 159+34, 1539)-Net over F4 — Constructive and digital
Digital (159, 193, 1539)-net over F4, using
- t-expansion [i] based on digital (158, 193, 1539)-net over F4, using
- 2 times m-reduction [i] based on digital (158, 195, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 65, 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, 65, 513)-net over F64, using
- 2 times m-reduction [i] based on digital (158, 195, 1539)-net over F4, using
(159, 159+34, 16447)-Net over F4 — Digital
Digital (159, 193, 16447)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4193, 16447, F4, 34) (dual of [16447, 16254, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(417, 63, F4, 8) (dual of [63, 46, 9]-code), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
(159, 159+34, large)-Net in Base 4 — Upper bound on s
There is no (159, 193, large)-net in base 4, because
- 32 times m-reduction [i] would yield (159, 161, large)-net in base 4, but