Best Known (42−30, 42, s)-Nets in Base 4
(42−30, 42, 28)-Net over F4 — Constructive and digital
Digital (12, 42, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
(42−30, 42, 29)-Net over F4 — Digital
Digital (12, 42, 29)-net over F4, using
- net from sequence [i] based on digital (12, 28)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 29, using
(42−30, 42, 87)-Net in Base 4 — Upper bound on s
There is no (12, 42, 88)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(442, 88, S4, 30), but
- the linear programming bound shows that M ≥ 89 605050 492137 134852 017163 586838 439030 395196 856884 186345 777644 655144 707653 985466 546419 715121 697993 523200 / 4 627392 744873 205288 863270 778823 516250 097275 954094 267550 824480 805099 989747 440773 > 442 [i]