Best Known (81−52, 81, s)-Nets in Base 27
(81−52, 81, 114)-Net over F27 — Constructive and digital
Digital (29, 81, 114)-net over F27, using
- t-expansion [i] based on digital (23, 81, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(81−52, 81, 172)-Net in Base 27 — Constructive
(29, 81, 172)-net in base 27, using
- 7 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 66, 172)-net over F81, using
(81−52, 81, 208)-Net over F27 — Digital
Digital (29, 81, 208)-net over F27, using
- t-expansion [i] based on digital (24, 81, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(81−52, 81, 226)-Net in Base 27
(29, 81, 226)-net in base 27, using
- 3 times m-reduction [i] based on (29, 84, 226)-net in base 27, using
- base change [i] based on digital (8, 63, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- base change [i] based on digital (8, 63, 226)-net over F81, using
(81−52, 81, 11669)-Net in Base 27 — Upper bound on s
There is no (29, 81, 11670)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 87 213086 426461 264130 671501 340161 909462 627000 235656 248624 771705 797847 821529 336495 619273 939806 699026 591365 495449 001533 > 2781 [i]