Best Known (28, 37, s)-Nets in Base 4
(28, 37, 1028)-Net over F4 — Constructive and digital
Digital (28, 37, 1028)-net over F4, using
- 41 times duplication [i] based on digital (27, 36, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 9, 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, 9, 257)-net over F256, using
(28, 37, 2048)-Net over F4 — Digital
Digital (28, 37, 2048)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(437, 2048, F4, 2, 9) (dual of [(2048, 2), 4059, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(437, 4096, F4, 9) (dual of [4096, 4059, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 2-folding [i] based on linear OA(437, 4096, F4, 9) (dual of [4096, 4059, 10]-code), using
(28, 37, 193403)-Net in Base 4 — Upper bound on s
There is no (28, 37, 193404)-net in base 4, because
- 1 times m-reduction [i] would yield (28, 36, 193404)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 4722 381121 003900 374934 > 436 [i]