Best Known (160, 160+44, s)-Nets in Base 4
(160, 160+44, 1056)-Net over F4 — Constructive and digital
Digital (160, 204, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 51, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(160, 160+44, 4190)-Net over F4 — Digital
Digital (160, 204, 4190)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4204, 4190, F4, 44) (dual of [4190, 3986, 45]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 43 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
- 1 times truncation [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- 1 times truncation [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 43 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
(160, 160+44, 1154684)-Net in Base 4 — Upper bound on s
There is no (160, 204, 1154685)-net in base 4, because
- 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]