Best Known (47, 47+17, s)-Nets in Base 3
(47, 47+17, 192)-Net over F3 — Constructive and digital
Digital (47, 64, 192)-net over F3, using
- 31 times duplication [i] based on digital (46, 63, 192)-net over F3, using
- trace code for nets [i] based on digital (4, 21, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- trace code for nets [i] based on digital (4, 21, 64)-net over F27, using
(47, 47+17, 311)-Net over F3 — Digital
Digital (47, 64, 311)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(364, 311, F3, 17) (dual of [311, 247, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(364, 364, F3, 17) (dual of [364, 300, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 364 | 36−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(364, 364, F3, 17) (dual of [364, 300, 18]-code), using
(47, 47+17, 10756)-Net in Base 3 — Upper bound on s
There is no (47, 64, 10757)-net in base 3, because
- 1 times m-reduction [i] would yield (47, 63, 10757)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 144641 876636 411999 511765 384545 > 363 [i]