Best Known (126, 162, s)-Nets in Base 4
(126, 162, 1044)-Net over F4 — Constructive and digital
Digital (126, 162, 1044)-net over F4, using
- 42 times duplication [i] based on digital (124, 160, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 40, 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, 40, 261)-net over F256, using
(126, 162, 3174)-Net over F4 — Digital
Digital (126, 162, 3174)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4162, 3174, F4, 36) (dual of [3174, 3012, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
(126, 162, 659992)-Net in Base 4 — Upper bound on s
There is no (126, 162, 659993)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 34 176000 348601 568826 503314 402030 435527 905141 169973 099684 860674 773567 346410 708644 393690 201397 568020 > 4162 [i]