Best Known (105−81, 105, s)-Nets in Base 27
(105−81, 105, 114)-Net over F27 — Constructive and digital
Digital (24, 105, 114)-net over F27, using
- t-expansion [i] based on digital (23, 105, 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
(105−81, 105, 208)-Net over F27 — Digital
Digital (24, 105, 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
(105−81, 105, 3173)-Net in Base 27 — Upper bound on s
There is no (24, 105, 3174)-net in base 27, because
- 1 times m-reduction [i] would yield (24, 104, 3174)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 73479 518233 916980 492910 648604 674620 805694 600021 295539 462952 270502 807358 728149 772167 003244 972652 982703 269298 464127 363308 029219 573612 905736 641693 729553 > 27104 [i]