Best Known (39−30, 39, s)-Nets in Base 4
(39−30, 39, 22)-Net over F4 — Constructive and digital
Digital (9, 39, 22)-net over F4, using
- net from sequence [i] based on digital (9, 21)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 9 and N(F) ≥ 22, using
(39−30, 39, 26)-Net over F4 — Digital
Digital (9, 39, 26)-net over F4, using
- net from sequence [i] based on digital (9, 25)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 9 and N(F) ≥ 26, using
(39−30, 39, 44)-Net over F4 — Upper bound on s (digital)
There is no digital (9, 39, 45)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(439, 45, F4, 30) (dual of [45, 6, 31]-code), but
(39−30, 39, 47)-Net in Base 4 — Upper bound on s
There is no (9, 39, 48)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(439, 48, S4, 30), but
- the linear programming bound shows that M ≥ 158456 325028 528675 187087 900672 / 329189 > 439 [i]