Best Known (27, 27+29, s)-Nets in Base 4
(27, 27+29, 41)-Net over F4 — Constructive and digital
Digital (27, 56, 41)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (10, 39, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (3, 17, 14)-net over F4, using
(27, 27+29, 42)-Net in Base 4 — Constructive
(27, 56, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
(27, 27+29, 55)-Net over F4 — Digital
Digital (27, 56, 55)-net over F4, using
- t-expansion [i] based on digital (26, 56, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
(27, 27+29, 456)-Net in Base 4 — Upper bound on s
There is no (27, 56, 457)-net in base 4, because
- 1 times m-reduction [i] would yield (27, 55, 457)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1329 119237 578707 184819 838701 541920 > 455 [i]