Best Known (56, 56+17, s)-Nets in Base 4
(56, 56+17, 1032)-Net over F4 — Constructive and digital
Digital (56, 73, 1032)-net over F4, using
- 41 times duplication [i] based on digital (55, 72, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
(56, 56+17, 2048)-Net over F4 — Digital
Digital (56, 73, 2048)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(473, 2048, F4, 2, 17) (dual of [(2048, 2), 4023, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(473, 4096, F4, 17) (dual of [4096, 4023, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 2-folding [i] based on linear OA(473, 4096, F4, 17) (dual of [4096, 4023, 18]-code), using
(56, 56+17, 328927)-Net in Base 4 — Upper bound on s
There is no (56, 73, 328928)-net in base 4, because
- 1 times m-reduction [i] would yield (56, 72, 328928)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 22 300849 390372 668778 816063 823679 858277 107085 > 472 [i]