Best Known (153, 153+40, s)-Nets in Base 4
(153, 153+40, 1060)-Net over F4 — Constructive and digital
Digital (153, 193, 1060)-net over F4, using
- 41 times duplication [i] based on digital (152, 192, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 48, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 48, 265)-net over F256, using
(153, 153+40, 4915)-Net over F4 — Digital
Digital (153, 193, 4915)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4193, 4915, F4, 40) (dual of [4915, 4722, 41]-code), using
- 806 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 17 times 0, 1, 32 times 0, 1, 57 times 0, 1, 89 times 0, 1, 120 times 0, 1, 143 times 0, 1, 157 times 0, 1, 167 times 0) [i] based on linear OA(4180, 4096, F4, 40) (dual of [4096, 3916, 41]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
- 806 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 17 times 0, 1, 32 times 0, 1, 57 times 0, 1, 89 times 0, 1, 120 times 0, 1, 143 times 0, 1, 157 times 0, 1, 167 times 0) [i] based on linear OA(4180, 4096, F4, 40) (dual of [4096, 3916, 41]-code), using
(153, 153+40, 1786734)-Net in Base 4 — Upper bound on s
There is no (153, 193, 1786735)-net in base 4, because
- 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]