Best Known (153, 153+41, s)-Nets in Base 4
(153, 153+41, 1056)-Net over F4 — Constructive and digital
Digital (153, 194, 1056)-net over F4, using
- 42 times duplication [i] based on 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
- trace code for nets [i] based on digital (7, 48, 264)-net over F256, using
(153, 153+41, 4444)-Net over F4 — Digital
Digital (153, 194, 4444)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4194, 4444, F4, 41) (dual of [4444, 4250, 42]-code), using
- 334 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, 1, 76 times 0, 1, 101 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]
- 334 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, 1, 76 times 0, 1, 101 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
(153, 153+41, 1786734)-Net in Base 4 — Upper bound on s
There is no (153, 194, 1786735)-net in base 4, because
- 1 times m-reduction [i] would yield (153, 193, 1786735)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 157 609345 005646 973477 206877 913634 275452 303448 726755 421631 171960 849283 900942 790270 639534 433946 249017 772316 421829 358814 > 4193 [i]