Best Known (159, 203, s)-Nets in Base 4
(159, 203, 1052)-Net over F4 — Constructive and digital
Digital (159, 203, 1052)-net over F4, using
- 1 times m-reduction [i] based on digital (159, 204, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 51, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 51, 263)-net over F256, using
(159, 203, 4145)-Net over F4 — Digital
Digital (159, 203, 4145)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4203, 4145, F4, 44) (dual of [4145, 3942, 45]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
(159, 203, 1084167)-Net in Base 4 — Upper bound on s
There is no (159, 203, 1084168)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 165 265815 531463 438521 706972 529801 309677 455545 361932 238403 642004 618308 267763 431378 389031 554190 569690 656155 413736 227940 381552 > 4203 [i]