Best Known (37, 103, s)-Nets in Base 27
(37, 103, 114)-Net over F27 — Constructive and digital
Digital (37, 103, 114)-net over F27, using
- t-expansion [i] based on digital (23, 103, 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
(37, 103, 172)-Net in Base 27 — Constructive
(37, 103, 172)-net in base 27, using
- t-expansion [i] based on (34, 103, 172)-net in base 27, using
- 5 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
- 5 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
(37, 103, 244)-Net over F27 — Digital
Digital (37, 103, 244)-net over F27, using
- t-expansion [i] based on digital (36, 103, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
(37, 103, 14841)-Net in Base 27 — Upper bound on s
There is no (37, 103, 14842)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2699 891984 060214 964656 349295 120722 105396 246694 000364 877779 888879 448235 090618 778173 236753 024692 218076 702802 497326 413238 484482 650921 667363 173075 647525 > 27103 [i]