Best Known (178, 220, s)-Nets in Base 3
(178, 220, 896)-Net over F3 — Constructive and digital
Digital (178, 220, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 55, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(178, 220, 3191)-Net over F3 — Digital
Digital (178, 220, 3191)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3220, 3191, F3, 42) (dual of [3191, 2971, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3220, 3280, F3, 42) (dual of [3280, 3060, 43]-code), using
- 1 times truncation [i] based on linear OA(3221, 3281, F3, 43) (dual of [3281, 3060, 44]-code), using
- an extension Ce(42) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- 1 times truncation [i] based on linear OA(3221, 3281, F3, 43) (dual of [3281, 3060, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(3220, 3280, F3, 42) (dual of [3280, 3060, 43]-code), using
(178, 220, 432369)-Net in Base 3 — Upper bound on s
There is no (178, 220, 432370)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 926 157831 409540 382616 665976 373415 500263 107092 184480 307125 492764 041294 256423 364814 971355 581562 670076 695773 > 3220 [i]