Best Known (56, 109, s)-Nets in Base 27
(56, 109, 204)-Net over F27 — Constructive and digital
Digital (56, 109, 204)-net over F27, using
- 1 times m-reduction [i] based on digital (56, 110, 204)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (11, 38, 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
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- digital (18, 72, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- digital (11, 38, 96)-net over F27, using
- (u, u+v)-construction [i] based on
(56, 109, 370)-Net in Base 27 — Constructive
(56, 109, 370)-net in base 27, using
- 271 times duplication [i] based on (55, 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
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
(56, 109, 797)-Net over F27 — Digital
Digital (56, 109, 797)-net over F27, using
(56, 109, 358070)-Net in Base 27 — Upper bound on s
There is no (56, 109, 358071)-net in base 27, because
- 1 times m-reduction [i] would yield (56, 108, 358071)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 38664 429324 046345 869316 656641 578417 502799 737841 849714 655565 701739 436608 020416 952572 247575 661741 425803 606911 820638 270926 100908 265661 367713 133337 445739 832653 > 27108 [i]