Best Known (170, 170+45, s)-Nets in Base 4
(170, 170+45, 1060)-Net over F4 — Constructive and digital
Digital (170, 215, 1060)-net over F4, using
- 1 times m-reduction [i] based on digital (170, 216, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 54, 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, 54, 265)-net over F256, using
(170, 170+45, 5054)-Net over F4 — Digital
Digital (170, 215, 5054)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4215, 5054, F4, 45) (dual of [5054, 4839, 46]-code), using
- 942 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, 1, 153 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]
- 942 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, 1, 153 times 0) [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
(170, 170+45, 2168352)-Net in Base 4 — Upper bound on s
There is no (170, 215, 2168353)-net in base 4, because
- 1 times m-reduction [i] would yield (170, 214, 2168353)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 693 169211 649694 764932 269936 422890 402461 186368 594188 358116 413842 297711 966548 829141 182864 283129 169066 108027 386486 592977 648335 700208 > 4214 [i]