Best Known (23−18, 23, s)-Nets in Base 4
(23−18, 23, 17)-Net over F4 — Constructive and digital
Digital (5, 23, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
(23−18, 23, 26)-Net over F4 — Upper bound on s (digital)
There is no digital (5, 23, 27)-net over F4, because
- 1 times m-reduction [i] would yield digital (5, 22, 27)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(422, 27, F4, 17) (dual of [27, 5, 18]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(422, 27, F4, 17) (dual of [27, 5, 18]-code), but
(23−18, 23, 33)-Net in Base 4 — Upper bound on s
There is no (5, 23, 34)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(423, 34, S4, 18), but
- the linear programming bound shows that M ≥ 2 882303 761517 117440 / 40641 > 423 [i]