Best Known (39, 39+12, s)-Nets in Base 4
(39, 39+12, 1028)-Net over F4 — Constructive and digital
Digital (39, 51, 1028)-net over F4, using
- 1 times m-reduction [i] based on digital (39, 52, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 13, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 13, 257)-net over F256, using
(39, 39+12, 1132)-Net over F4 — Digital
Digital (39, 51, 1132)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(451, 1132, F4, 12) (dual of [1132, 1081, 13]-code), using
- 103 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 27 times 0, 1, 50 times 0) [i] based on linear OA(445, 1023, F4, 12) (dual of [1023, 978, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 103 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 27 times 0, 1, 50 times 0) [i] based on linear OA(445, 1023, F4, 12) (dual of [1023, 978, 13]-code), using
(39, 39+12, 130796)-Net in Base 4 — Upper bound on s
There is no (39, 51, 130797)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 5 070740 399291 502070 389358 218172 > 451 [i]