Best Known (121, 154, s)-Nets in Base 4
(121, 154, 1048)-Net over F4 — Constructive and digital
Digital (121, 154, 1048)-net over F4, using
- 42 times duplication [i] based on digital (119, 152, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 38, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 38, 262)-net over F256, using
(121, 154, 3851)-Net over F4 — Digital
Digital (121, 154, 3851)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4154, 3851, F4, 33) (dual of [3851, 3697, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4154, 4121, F4, 33) (dual of [4121, 3967, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- linear OA(4145, 4097, F4, 33) (dual of [4097, 3952, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4121, 4097, F4, 27) (dual of [4097, 3976, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(49, 24, F4, 5) (dual of [24, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 36, F4, 5) (dual of [36, 27, 6]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4154, 4121, F4, 33) (dual of [4121, 3967, 34]-code), using
(121, 154, 1296020)-Net in Base 4 — Upper bound on s
There is no (121, 154, 1296021)-net in base 4, because
- 1 times m-reduction [i] would yield (121, 153, 1296021)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 130 371273 094289 026686 639282 344053 070644 343197 765425 665626 106736 407140 997580 021289 180085 189509 > 4153 [i]