Best Known (74−53, 74, s)-Nets in Base 3
(74−53, 74, 32)-Net over F3 — Constructive and digital
Digital (21, 74, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
(74−53, 74, 70)-Net over F3 — Upper bound on s (digital)
There is no digital (21, 74, 71)-net over F3, because
- 8 times m-reduction [i] would yield digital (21, 66, 71)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(366, 71, F3, 45) (dual of [71, 5, 46]-code), but
- “HW1†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(366, 71, F3, 45) (dual of [71, 5, 46]-code), but
(74−53, 74, 73)-Net in Base 3 — Upper bound on s
There is no (21, 74, 74)-net in base 3, because
- 11 times m-reduction [i] would yield (21, 63, 74)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(363, 74, S3, 42), but
- the linear programming bound shows that M ≥ 12 034337 282839 174538 591498 251772 066709 / 10 069525 > 363 [i]
- extracting embedded orthogonal array [i] would yield OA(363, 74, S3, 42), but