Best Known (99−56, 99, s)-Nets in Base 27
(99−56, 99, 166)-Net over F27 — Constructive and digital
Digital (43, 99, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (8, 64, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 35, 82)-net over F27, using
(99−56, 99, 299)-Net over F27 — Digital
Digital (43, 99, 299)-net over F27, using
(99−56, 99, 370)-Net in Base 27 — Constructive
(43, 99, 370)-net in base 27, using
- 9 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
(99−56, 99, 49980)-Net in Base 27 — Upper bound on s
There is no (43, 99, 49981)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 5072 207927 941926 556230 603886 768793 423395 397188 839600 249711 761271 527535 100070 453054 288315 914120 182736 491450 020921 840431 970879 429196 679231 975953 > 2799 [i]