Best Known (72−37, 72, s)-Nets in Base 27
(72−37, 72, 176)-Net over F27 — Constructive and digital
Digital (35, 72, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (10, 47, 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
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (7, 25, 82)-net over F27, using
(72−37, 72, 370)-Net in Base 27 — Constructive
(35, 72, 370)-net in base 27, using
- 4 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
(72−37, 72, 413)-Net over F27 — Digital
Digital (35, 72, 413)-net over F27, using
(72−37, 72, 128546)-Net in Base 27 — Upper bound on s
There is no (35, 72, 128547)-net in base 27, because
- 1 times m-reduction [i] would yield (35, 71, 128547)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 423499 834722 998851 715062 942833 908722 740518 206379 554895 071909 345685 556411 135836 216073 637624 456179 823765 > 2771 [i]