Best Known (205−45, 205, s)-Nets in Base 4
(205−45, 205, 1052)-Net over F4 — Constructive and digital
Digital (160, 205, 1052)-net over F4, using
- 41 times duplication [i] based on digital (159, 204, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 51, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 51, 263)-net over F256, using
(205−45, 205, 4008)-Net over F4 — Digital
Digital (160, 205, 4008)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4205, 4008, F4, 45) (dual of [4008, 3803, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(4205, 4097, F4, 45) (dual of [4097, 3892, 46]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4205, 4097, F4, 45) (dual of [4097, 3892, 46]-code), using
(205−45, 205, 1154684)-Net in Base 4 — Upper bound on s
There is no (160, 205, 1154685)-net in base 4, because
- 1 times m-reduction [i] would yield (160, 204, 1154685)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 661 067950 715044 836365 328982 415234 875998 119063 039966 504452 915327 924770 920405 821381 353234 351535 498772 783734 844159 016627 804364 > 4204 [i]