Best Known (32, 32+78, s)-Nets in Base 27
(32, 32+78, 114)-Net over F27 — Constructive and digital
Digital (32, 110, 114)-net over F27, using
- t-expansion [i] based on digital (23, 110, 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
(32, 32+78, 116)-Net in Base 27 — Constructive
(32, 110, 116)-net in base 27, using
- 272 times duplication [i] based on (30, 108, 116)-net in base 27, using
- t-expansion [i] based on (29, 108, 116)-net in base 27, using
- base change [i] based on digital (2, 81, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 81, 116)-net over F81, using
- t-expansion [i] based on (29, 108, 116)-net in base 27, using
(32, 32+78, 208)-Net over F27 — Digital
Digital (32, 110, 208)-net over F27, using
- t-expansion [i] based on digital (24, 110, 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
(32, 32+78, 6430)-Net in Base 27 — Upper bound on s
There is no (32, 110, 6431)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 28 255634 552433 057417 912237 076343 624705 988865 235892 823976 088498 077262 046597 916715 167549 488073 799612 753928 390793 563703 146812 927867 149854 070028 189163 157133 579147 > 27110 [i]