Best Known (61−15, 61, s)-Nets in Base 3
(61−15, 61, 328)-Net over F3 — Constructive and digital
Digital (46, 61, 328)-net over F3, using
- 31 times duplication [i] based on digital (45, 60, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 15, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 15, 82)-net over F81, using
(61−15, 61, 440)-Net over F3 — Digital
Digital (46, 61, 440)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(361, 440, F3, 15) (dual of [440, 379, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(361, 728, F3, 15) (dual of [728, 667, 16]-code), using
(61−15, 61, 20766)-Net in Base 3 — Upper bound on s
There is no (46, 61, 20767)-net in base 3, because
- 1 times m-reduction [i] would yield (46, 60, 20767)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 42398 161853 596749 335252 140659 > 360 [i]