Best Known (192−41, 192, s)-Nets in Base 4
(192−41, 192, 1056)-Net over F4 — Constructive and digital
Digital (151, 192, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 48, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(192−41, 192, 4263)-Net over F4 — Digital
Digital (151, 192, 4263)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4192, 4263, F4, 41) (dual of [4263, 4071, 42]-code), using
- 155 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0, 1, 37 times 0, 1, 54 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- 155 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0, 1, 37 times 0, 1, 54 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
(192−41, 192, 1555440)-Net in Base 4 — Upper bound on s
There is no (151, 192, 1555441)-net in base 4, because
- 1 times m-reduction [i] would yield (151, 191, 1555441)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 9 850575 455059 736577 310532 806241 601068 103037 711097 495488 405863 745647 498369 340388 771147 333156 849594 648679 106209 174904 > 4191 [i]