Best Known (241−53, 241, s)-Nets in Base 4
(241−53, 241, 1056)-Net over F4 — Constructive and digital
Digital (188, 241, 1056)-net over F4, using
- 41 times duplication [i] based on digital (187, 240, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 60, 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, 60, 264)-net over F256, using
(241−53, 241, 4233)-Net over F4 — Digital
Digital (188, 241, 4233)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4241, 4233, F4, 53) (dual of [4233, 3992, 54]-code), using
- 131 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 37 times 0, 1, 60 times 0) [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]
- 131 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 37 times 0, 1, 60 times 0) [i] based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
(241−53, 241, 1269525)-Net in Base 4 — Upper bound on s
There is no (188, 241, 1269526)-net in base 4, because
- 1 times m-reduction [i] would yield (188, 240, 1269526)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3 121788 306901 374488 944048 444527 233201 220972 899342 667909 015374 096879 689555 705276 925726 388552 319053 384144 354036 211331 848943 513522 397925 018491 828928 > 4240 [i]