Best Known (153−32, 153, s)-Nets in Base 4
(153−32, 153, 1052)-Net over F4 — Constructive and digital
Digital (121, 153, 1052)-net over F4, using
- 41 times duplication [i] based on digital (120, 152, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 38, 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, 38, 263)-net over F256, using
(153−32, 153, 4220)-Net over F4 — Digital
Digital (121, 153, 4220)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4153, 4220, F4, 32) (dual of [4220, 4067, 33]-code), using
- 115 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 17 times 0, 1, 29 times 0, 1, 46 times 0) [i] based on linear OA(4144, 4096, F4, 32) (dual of [4096, 3952, 33]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(4145, 4097, F4, 33) (dual of [4097, 3952, 34]-code), using
- 115 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 17 times 0, 1, 29 times 0, 1, 46 times 0) [i] based on linear OA(4144, 4096, F4, 32) (dual of [4096, 3952, 33]-code), using
(153−32, 153, 1296020)-Net in Base 4 — Upper bound on s
There is no (121, 153, 1296021)-net in base 4, because
- 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]