Best Known (40, 40+59, s)-Nets in Base 27
(40, 40+59, 146)-Net over F27 — Constructive and digital
Digital (40, 99, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 33, 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 (7, 66, 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, 33, 64)-net over F27, using
(40, 40+59, 224)-Net in Base 27 — Constructive
(40, 99, 224)-net in base 27, using
- 9 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
(40, 40+59, 273)-Net over F27 — Digital
Digital (40, 99, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
(40, 40+59, 298)-Net in Base 27
(40, 99, 298)-net in base 27, using
- t-expansion [i] based on (39, 99, 298)-net in base 27, using
- 9 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- 9 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(40, 40+59, 30828)-Net in Base 27 — Upper bound on s
There is no (40, 99, 30829)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 98, 30829)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 187 795355 437511 698987 706871 193402 540508 224121 060290 024723 055646 534688 547159 451258 333155 369266 351296 209276 277670 784867 481753 562904 601371 965155 > 2798 [i]