Best Known (129−33, 129, s)-Nets in Base 3
(129−33, 129, 282)-Net over F3 — Constructive and digital
Digital (96, 129, 282)-net over F3, using
- trace code for nets [i] based on digital (10, 43, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
(129−33, 129, 553)-Net over F3 — Digital
Digital (96, 129, 553)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3129, 553, F3, 33) (dual of [553, 424, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3129, 728, F3, 33) (dual of [728, 599, 34]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(3129, 728, F3, 33) (dual of [728, 599, 34]-code), using
(129−33, 129, 22293)-Net in Base 3 — Upper bound on s
There is no (96, 129, 22294)-net in base 3, because
- 1 times m-reduction [i] would yield (96, 128, 22294)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 11 794955 981214 144916 285077 540063 156236 763887 728083 070561 014945 > 3128 [i]