Best Known (10, 61, s)-Nets in Base 27
(10, 61, 94)-Net over F27 — Constructive and digital
Digital (10, 61, 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, 61, 99)-Net over F27 — Digital
Digital (10, 61, 99)-net over F27, using
- t-expansion [i] based on digital (9, 61, 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, 61, 1053)-Net in Base 27 — Upper bound on s
There is no (10, 61, 1054)-net in base 27, because
- 1 times m-reduction [i] would yield (10, 60, 1054)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 77 098466 004585 794870 280852 052915 403662 833223 248635 800280 622814 476901 521597 247666 515549 > 2760 [i]