Best Known (65−35, 65, s)-Nets in Base 4
(65−35, 65, 41)-Net over F4 — Constructive and digital
Digital (30, 65, 41)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 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, 45, 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, 20, 14)-net over F4, using
(65−35, 65, 43)-Net in Base 4 — Constructive
(30, 65, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
(65−35, 65, 55)-Net over F4 — Digital
Digital (30, 65, 55)-net over F4, using
- t-expansion [i] based on digital (26, 65, 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
(65−35, 65, 428)-Net in Base 4 — Upper bound on s
There is no (30, 65, 429)-net in base 4, because
- 1 times m-reduction [i] would yield (30, 64, 429)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 347 223829 516196 539955 194602 993066 330160 > 464 [i]