Best Known (76−53, 76, s)-Nets in Base 27
(76−53, 76, 114)-Net over F27 — Constructive and digital
Digital (23, 76, 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
(76−53, 76, 150)-Net in Base 27 — Constructive
(23, 76, 150)-net in base 27, using
- base change [i] based on digital (4, 57, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
(76−53, 76, 163)-Net over F27 — Digital
Digital (23, 76, 163)-net over F27, using
- t-expansion [i] based on digital (21, 76, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
(76−53, 76, 5447)-Net in Base 27 — Upper bound on s
There is no (23, 76, 5448)-net in base 27, because
- 1 times m-reduction [i] would yield (23, 75, 5448)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 225830 634585 774672 073646 630586 554732 308151 647811 352000 151677 366332 075618 967014 268151 781035 145468 993088 175281 > 2775 [i]