Best Known (13, 13+35, s)-Nets in Base 27
(13, 13+35, 96)-Net over F27 — Constructive and digital
Digital (13, 48, 96)-net over F27, using
- t-expansion [i] based on digital (11, 48, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(13, 13+35, 100)-Net in Base 27 — Constructive
(13, 48, 100)-net in base 27, using
- base change [i] based on digital (1, 36, 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
(13, 13+35, 136)-Net over F27 — Digital
Digital (13, 48, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(13, 13+35, 2493)-Net in Base 27 — Upper bound on s
There is no (13, 48, 2494)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 47, 2494)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 18 891706 995662 426029 076030 445958 635938 599470 316424 073693 844178 702637 > 2747 [i]