Best Known (237−52, 237, s)-Nets in Base 4
(237−52, 237, 1056)-Net over F4 — Constructive and digital
Digital (185, 237, 1056)-net over F4, using
- 41 times duplication [i] based on digital (184, 236, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 59, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
- trace code for nets [i] based on digital (7, 59, 264)-net over F256, using
(237−52, 237, 4204)-Net over F4 — Digital
Digital (185, 237, 4204)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4237, 4204, F4, 52) (dual of [4204, 3967, 53]-code), using
- 106 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
- 1 times truncation [i] based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
- an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- 1 times truncation [i] based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
- 106 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
(237−52, 237, 1081861)-Net in Base 4 — Upper bound on s
There is no (185, 237, 1081862)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 48777 894055 607090 872184 292349 961501 338676 430858 867088 057861 821860 324701 349696 627906 111717 903108 061604 933380 009170 223410 533976 200521 743693 218432 > 4237 [i]