Best Known (10, 10+25, s)-Nets in Base 27
(10, 10+25, 94)-Net over F27 — Constructive and digital
Digital (10, 35, 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
(10, 10+25, 99)-Net over F27 — Digital
Digital (10, 35, 99)-net over F27, using
- t-expansion [i] based on digital (9, 35, 99)-net over F27, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 99, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
(10, 10+25, 100)-Net in Base 27 — Constructive
(10, 35, 100)-net in base 27, using
- 1 times m-reduction [i] based on (10, 36, 100)-net in base 27, using
- base change [i] based on digital (1, 27, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 27, 100)-net over F81, using
(10, 10+25, 2305)-Net in Base 27 — Upper bound on s
There is no (10, 35, 2306)-net in base 27, because
- 1 times m-reduction [i] would yield (10, 34, 2306)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 4 646244 876133 940460 969665 140166 896648 425171 877497 > 2734 [i]