Best Known (51, 110, s)-Nets in Base 27
(51, 110, 192)-Net over F27 — Constructive and digital
Digital (51, 110, 192)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (11, 40, 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 (11, 70, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27 (see above)
- digital (11, 40, 96)-net over F27, using
(51, 110, 370)-Net in Base 27 — Constructive
(51, 110, 370)-net in base 27, using
- 272 times duplication [i] based on (49, 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
(51, 110, 440)-Net over F27 — Digital
Digital (51, 110, 440)-net over F27, using
(51, 110, 107656)-Net in Base 27 — Upper bound on s
There is no (51, 110, 107657)-net in base 27, because
- 1 times m-reduction [i] would yield (51, 109, 107657)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 043956 338304 604462 879669 493903 393785 358908 147253 793175 502921 924604 166207 304955 833673 051037 046614 149976 150783 880070 057476 005793 463667 327524 852667 151150 746139 > 27109 [i]