Best Known (57, 108, s)-Nets in Base 27
(57, 108, 210)-Net over F27 — Constructive and digital
Digital (57, 108, 210)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 21, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 29, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (7, 58, 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 (4, 21, 64)-net over F27, using
(57, 108, 370)-Net in Base 27 — Constructive
(57, 108, 370)-net in base 27, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
(57, 108, 951)-Net over F27 — Digital
Digital (57, 108, 951)-net over F27, using
(57, 108, 523454)-Net in Base 27 — Upper bound on s
There is no (57, 108, 523455)-net in base 27, because
- 1 times m-reduction [i] would yield (57, 107, 523455)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1431 992267 895991 611379 455385 834433 561202 733872 832791 081104 671098 495616 641093 500132 382376 858667 409381 109064 140346 545326 812544 420218 258023 229048 480120 066295 > 27107 [i]