Best Known (170, 170+46, s)-Nets in Base 4
(170, 170+46, 1060)-Net over F4 — Constructive and digital
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
(170, 170+46, 4586)-Net over F4 — Digital
Digital (170, 216, 4586)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4216, 4586, F4, 46) (dual of [4586, 4370, 47]-code), using
- 473 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 10 times 0, 1, 20 times 0, 1, 37 times 0, 1, 61 times 0, 1, 89 times 0, 1, 113 times 0, 1, 128 times 0) [i] based on linear OA(4205, 4102, F4, 46) (dual of [4102, 3897, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(44) [i] based on
- linear OA(4205, 4096, F4, 46) (dual of [4096, 3891, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- 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]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(45) ⊂ Ce(44) [i] based on
- 473 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 10 times 0, 1, 20 times 0, 1, 37 times 0, 1, 61 times 0, 1, 89 times 0, 1, 113 times 0, 1, 128 times 0) [i] based on linear OA(4205, 4102, F4, 46) (dual of [4102, 3897, 47]-code), using
(170, 170+46, 1417287)-Net in Base 4 — Upper bound on s
There is no (170, 216, 1417288)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 11090 790919 396111 214790 346552 652501 164368 176260 426131 276501 651822 378497 697633 359721 723465 908911 686813 721519 088352 267178 706669 032660 > 4216 [i]