Best Known (11, 11+69, s)-Nets in Base 27
(11, 11+69, 96)-Net over F27 — Constructive and digital
Digital (11, 80, 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
(11, 11+69, 100)-Net over F27 — Digital
Digital (11, 80, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(11, 11+69, 1084)-Net in Base 27 — Upper bound on s
There is no (11, 80, 1085)-net in base 27, because
- 1 times m-reduction [i] would yield (11, 79, 1085)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 121078 867260 877132 848412 053612 072820 988124 428811 092047 739692 535981 069567 965075 206862 811436 598424 557722 089184 647505 > 2779 [i]