Best Known (154, 154+41, s)-Nets in Base 4
(154, 154+41, 1056)-Net over F4 — Constructive and digital
Digital (154, 195, 1056)-net over F4, using
- 1 times m-reduction [i] based on digital (154, 196, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 49, 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, 49, 264)-net over F256, using
(154, 154+41, 4571)-Net over F4 — Digital
Digital (154, 195, 4571)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4195, 4571, F4, 41) (dual of [4571, 4376, 42]-code), using
- 460 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, 1, 125 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]
- 460 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, 1, 125 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
(154, 154+41, 1914975)-Net in Base 4 — Upper bound on s
There is no (154, 195, 1914976)-net in base 4, because
- 1 times m-reduction [i] would yield (154, 194, 1914976)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 630 435286 803731 798051 992352 210252 222610 321479 038526 452842 457296 992186 843989 109625 023737 028053 879940 330465 694397 345471 > 4194 [i]