Best Known (187−42, 187, s)-Nets in Base 4
(187−42, 187, 1044)-Net over F4 — Constructive and digital
Digital (145, 187, 1044)-net over F4, using
- 1 times m-reduction [i] based on digital (145, 188, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 47, 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, 47, 261)-net over F256, using
(187−42, 187, 3282)-Net over F4 — Digital
Digital (145, 187, 3282)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4187, 3282, F4, 42) (dual of [3282, 3095, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using
- an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- discarding factors / shortening the dual code based on linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using
(187−42, 187, 664601)-Net in Base 4 — Upper bound on s
There is no (145, 187, 664602)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 38479 572705 107068 117660 055350 388093 312375 664603 420138 110976 617117 993865 625351 672563 377726 593259 101946 440507 204582 > 4187 [i]