Best Known (124, 156, s)-Nets in Base 4
(124, 156, 1056)-Net over F4 — Constructive and digital
Digital (124, 156, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 39, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(124, 156, 4522)-Net over F4 — Digital
Digital (124, 156, 4522)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4156, 4522, F4, 32) (dual of [4522, 4366, 33]-code), using
- 414 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, 1, 68 times 0, 1, 98 times 0, 1, 130 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
- 414 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, 1, 68 times 0, 1, 98 times 0, 1, 130 times 0) [i] based on linear OA(4144, 4096, F4, 32) (dual of [4096, 3952, 33]-code), using
(124, 156, 1680734)-Net in Base 4 — Upper bound on s
There is no (124, 156, 1680735)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8343 753068 619609 088732 126485 985458 547076 917165 681604 549107 900526 592139 549018 994693 911331 030743 > 4156 [i]