Best Known (208−45, 208, s)-Nets in Base 4
(208−45, 208, 1056)-Net over F4 — Constructive and digital
Digital (163, 208, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 52, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(208−45, 208, 4219)-Net over F4 — Digital
Digital (163, 208, 4219)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4208, 4219, F4, 45) (dual of [4219, 4011, 46]-code), using
- 114 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, 45 times 0) [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- 114 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, 45 times 0) [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
(208−45, 208, 1394965)-Net in Base 4 — Upper bound on s
There is no (163, 208, 1394966)-net in base 4, because
- 1 times m-reduction [i] would yield (163, 207, 1394966)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 42308 034578 658922 981271 632478 101677 193405 706129 656138 280431 689867 812265 908328 248078 373883 998364 803516 307308 406942 492469 833144 > 4207 [i]