Best Known (169, 214, s)-Nets in Base 4
(169, 214, 1060)-Net over F4 — Constructive and digital
Digital (169, 214, 1060)-net over F4, using
- 42 times duplication [i] based on digital (167, 212, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 53, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 53, 265)-net over F256, using
(169, 214, 4899)-Net over F4 — Digital
Digital (169, 214, 4899)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4214, 4899, F4, 45) (dual of [4899, 4685, 46]-code), using
- 788 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, 1, 64 times 0, 1, 86 times 0, 1, 108 times 0, 1, 126 times 0, 1, 137 times 0, 1, 147 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]
- 788 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, 1, 64 times 0, 1, 86 times 0, 1, 108 times 0, 1, 126 times 0, 1, 137 times 0, 1, 147 times 0) [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
(169, 214, 2035932)-Net in Base 4 — Upper bound on s
There is no (169, 214, 2035933)-net in base 4, because
- 1 times m-reduction [i] would yield (169, 213, 2035933)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 173 293112 105949 147324 957589 125146 249745 039008 364666 357655 112879 307409 579974 984266 564958 932042 484741 556080 708776 876667 145889 613412 > 4213 [i]