Best Known (31−21, 31, s)-Nets in Base 27
(31−21, 31, 94)-Net over F27 — Constructive and digital
Digital (10, 31, 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
(31−21, 31, 99)-Net over F27 — Digital
Digital (10, 31, 99)-net over F27, using
- t-expansion [i] based on digital (9, 31, 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
(31−21, 31, 116)-Net in Base 27 — Constructive
(10, 31, 116)-net in base 27, using
- 1 times m-reduction [i] based on (10, 32, 116)-net in base 27, using
- base change [i] based on digital (2, 24, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 24, 116)-net over F81, using
(31−21, 31, 118)-Net in Base 27
(10, 31, 118)-net in base 27, using
- 1 times m-reduction [i] based on (10, 32, 118)-net in base 27, using
- base change [i] based on digital (2, 24, 118)-net over F81, using
- net from sequence [i] based on digital (2, 117)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 118, using
- net from sequence [i] based on digital (2, 117)-sequence over F81, using
- base change [i] based on digital (2, 24, 118)-net over F81, using
(31−21, 31, 3423)-Net in Base 27 — Upper bound on s
There is no (10, 31, 3424)-net in base 27, because
- 1 times m-reduction [i] would yield (10, 30, 3424)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 8 739708 948738 591039 218685 107864 369282 930241 > 2730 [i]