Best Known (211−47, 211, s)-Nets in Base 4
(211−47, 211, 1048)-Net over F4 — Constructive and digital
Digital (164, 211, 1048)-net over F4, using
- 1 times m-reduction [i] based on digital (164, 212, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 53, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 53, 262)-net over F256, using
(211−47, 211, 3755)-Net over F4 — Digital
Digital (164, 211, 3755)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4211, 3755, F4, 47) (dual of [3755, 3544, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(4211, 4096, F4, 47) (dual of [4096, 3885, 48]-code), using
- an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- discarding factors / shortening the dual code based on linear OA(4211, 4096, F4, 47) (dual of [4096, 3885, 48]-code), using
(211−47, 211, 987179)-Net in Base 4 — Upper bound on s
There is no (164, 211, 987180)-net in base 4, because
- 1 times m-reduction [i] would yield (164, 210, 987180)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 707692 309835 203242 182564 322347 209034 351595 021827 010151 379878 193823 643541 290882 046277 816375 340227 491152 469790 631660 696016 876276 > 4210 [i]