Best Known (49−12, 49, s)-Nets in Base 4
(49−12, 49, 1028)-Net over F4 — Constructive and digital
Digital (37, 49, 1028)-net over F4, using
- 41 times duplication [i] based on digital (36, 48, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 12, 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, 12, 257)-net over F256, using
(49−12, 49, 1051)-Net over F4 — Digital
Digital (37, 49, 1051)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(449, 1051, F4, 12) (dual of [1051, 1002, 13]-code), using
- 24 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 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]
- 24 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 times 0) [i] based on linear OA(445, 1023, F4, 12) (dual of [1023, 978, 13]-code), using
(49−12, 49, 82394)-Net in Base 4 — Upper bound on s
There is no (37, 49, 82395)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 316914 775106 740761 253432 240918 > 449 [i]