Best Known (154, 199, s)-Nets in Base 4
(154, 199, 1044)-Net over F4 — Constructive and digital
Digital (154, 199, 1044)-net over F4, using
- 1 times m-reduction [i] based on digital (154, 200, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 50, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 50, 261)-net over F256, using
(154, 199, 3298)-Net over F4 — Digital
Digital (154, 199, 3298)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4199, 3298, F4, 45) (dual of [3298, 3099, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- discarding factors / shortening the dual code based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
(154, 199, 791155)-Net in Base 4 — Upper bound on s
There is no (154, 199, 791156)-net in base 4, because
- 1 times m-reduction [i] would yield (154, 198, 791156)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 161392 424704 596040 169300 147761 151662 724800 536675 651127 487050 248068 649370 350584 694784 241981 256177 333859 459041 923370 351064 > 4198 [i]