Best Known (152, 192, s)-Nets in Base 4
(152, 192, 1060)-Net over F4 — Constructive and digital
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
(152, 192, 4746)-Net over F4 — Digital
Digital (152, 192, 4746)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4192, 4746, F4, 40) (dual of [4746, 4554, 41]-code), using
- 638 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) [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
- 638 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) [i] based on linear OA(4180, 4096, F4, 40) (dual of [4096, 3916, 41]-code), using
(152, 192, 1667080)-Net in Base 4 — Upper bound on s
There is no (152, 192, 1667081)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 39 402043 407416 610926 824713 195989 848818 035894 418581 456937 453346 742092 013613 461755 120603 306660 105072 538659 415006 508544 > 4192 [i]