Best Known (152−32, 152, s)-Nets in Base 4
(152−32, 152, 1052)-Net over F4 — Constructive and digital
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
(152−32, 152, 4172)-Net over F4 — Digital
Digital (120, 152, 4172)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4152, 4172, F4, 32) (dual of [4172, 4020, 33]-code), using
- 68 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) [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
- 68 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) [i] based on linear OA(4144, 4096, F4, 32) (dual of [4096, 3952, 33]-code), using
(152−32, 152, 1188454)-Net in Base 4 — Upper bound on s
There is no (120, 152, 1188455)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 32 592628 730172 633741 824844 247844 442854 396388 372649 120603 950191 781561 911915 362347 907281 160234 > 4152 [i]