Best Known (166, 166+44, s)-Nets in Base 4
(166, 166+44, 1060)-Net over F4 — Constructive and digital
Digital (166, 210, 1060)-net over F4, using
- 42 times duplication [i] based on digital (164, 208, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 52, 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, 52, 265)-net over F256, using
(166, 166+44, 4927)-Net over F4 — Digital
Digital (166, 210, 4927)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4210, 4927, F4, 44) (dual of [4927, 4717, 45]-code), using
- 820 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 43 times 0, 1, 69 times 0, 1, 98 times 0, 1, 122 times 0, 1, 137 times 0, 1, 146 times 0, 1, 153 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
- 820 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 43 times 0, 1, 69 times 0, 1, 98 times 0, 1, 122 times 0, 1, 137 times 0, 1, 146 times 0, 1, 153 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
(166, 166+44, 1685246)-Net in Base 4 — Upper bound on s
There is no (166, 210, 1685247)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 707699 692436 455692 302489 759339 697537 000222 881237 379216 642773 753828 971958 733229 680186 583958 140843 663704 362068 405428 649366 512335 > 4210 [i]