Best Known (160−33, 160, s)-Nets in Base 4
(160−33, 160, 1056)-Net over F4 — Constructive and digital
Digital (127, 160, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 40, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(160−33, 160, 4498)-Net over F4 — Digital
Digital (127, 160, 4498)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4160, 4498, F4, 33) (dual of [4498, 4338, 34]-code), using
- 386 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 12 times 0, 1, 18 times 0, 1, 29 times 0, 1, 43 times 0, 1, 62 times 0, 1, 85 times 0, 1, 113 times 0) [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]
- 386 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 12 times 0, 1, 18 times 0, 1, 29 times 0, 1, 43 times 0, 1, 62 times 0, 1, 85 times 0, 1, 113 times 0) [i] based on linear OA(4145, 4097, F4, 33) (dual of [4097, 3952, 34]-code), using
(160−33, 160, 2179646)-Net in Base 4 — Upper bound on s
There is no (127, 160, 2179647)-net in base 4, because
- 1 times m-reduction [i] would yield (127, 159, 2179647)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 533998 478282 903718 992097 639569 453155 109075 496349 869707 776474 694813 364670 263232 304979 940147 027717 > 4159 [i]