Best Known (13, 13+6, s)-Nets in Base 3
(13, 13+6, 84)-Net over F3 — Constructive and digital
Digital (13, 19, 84)-net over F3, using
- 31 times duplication [i] based on digital (12, 18, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 6, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 6, 28)-net over F27, using
(13, 13+6, 121)-Net over F3 — Digital
Digital (13, 19, 121)-net over F3, using
- net defined by OOA [i] based on linear OOA(319, 121, F3, 6, 6) (dual of [(121, 6), 707, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(319, 121, F3, 5, 6) (dual of [(121, 5), 586, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(319, 121, F3, 6) (dual of [121, 102, 7]-code), using
- 1 times truncation [i] based on linear OA(320, 122, F3, 7) (dual of [122, 102, 8]-code), using
- a “DaH†code from Brouwer’s database [i]
- 1 times truncation [i] based on linear OA(320, 122, F3, 7) (dual of [122, 102, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(319, 121, F3, 6) (dual of [121, 102, 7]-code), using
- appending kth column [i] based on linear OOA(319, 121, F3, 5, 6) (dual of [(121, 5), 586, 7]-NRT-code), using
(13, 13+6, 952)-Net in Base 3 — Upper bound on s
There is no (13, 19, 953)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1163 126971 > 319 [i]