Best Known (199, 246, s)-Nets in Base 4
(199, 246, 1539)-Net over F4 — Constructive and digital
Digital (199, 246, 1539)-net over F4, using
- t-expansion [i] based on digital (198, 246, 1539)-net over F4, using
- 9 times m-reduction [i] based on digital (198, 255, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 85, 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, 85, 513)-net over F64, using
- 9 times m-reduction [i] based on digital (198, 255, 1539)-net over F4, using
(199, 246, 11105)-Net over F4 — Digital
Digital (199, 246, 11105)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4246, 11105, F4, 47) (dual of [11105, 10859, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(4246, 16384, F4, 47) (dual of [16384, 16138, 48]-code), using
- an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- discarding factors / shortening the dual code based on linear OA(4246, 16384, F4, 47) (dual of [16384, 16138, 48]-code), using
(199, 246, 8139200)-Net in Base 4 — Upper bound on s
There is no (199, 246, 8139201)-net in base 4, because
- 1 times m-reduction [i] would yield (199, 245, 8139201)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3196 672407 784446 524771 019476 780387 602099 206439 241068 374781 550130 397892 550033 411837 286742 703225 966649 655914 024068 400368 997494 364977 696719 252788 853824 > 4245 [i]