Best Known (158, 202, s)-Nets in Base 4
(158, 202, 1052)-Net over F4 — Constructive and digital
Digital (158, 202, 1052)-net over F4, using
- 42 times duplication [i] based on digital (156, 200, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 50, 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, 50, 263)-net over F256, using
(158, 202, 4120)-Net over F4 — Digital
Digital (158, 202, 4120)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4202, 4120, F4, 44) (dual of [4120, 3918, 45]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 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
- 21 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
(158, 202, 1017957)-Net in Base 4 — Upper bound on s
There is no (158, 202, 1017958)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 41 316669 522270 717073 664215 087899 341984 631047 937844 285796 374039 680793 134350 606296 174680 822555 297670 250439 602870 483667 417952 > 4202 [i]