Best Known (87, 117, s)-Nets in Base 3
(87, 117, 264)-Net over F3 — Constructive and digital
Digital (87, 117, 264)-net over F3, using
- trace code for nets [i] based on digital (9, 39, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
(87, 117, 511)-Net over F3 — Digital
Digital (87, 117, 511)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3117, 511, F3, 30) (dual of [511, 394, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 728, F3, 30) (dual of [728, 611, 31]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(3117, 728, F3, 30) (dual of [728, 611, 31]-code), using
(87, 117, 16900)-Net in Base 3 — Upper bound on s
There is no (87, 117, 16901)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 66 561164 543649 824291 267112 628800 487559 990838 827447 763067 > 3117 [i]