Best Known (42, 93, s)-Nets in Base 2
(42, 93, 33)-Net over F2 — Constructive and digital
Digital (42, 93, 33)-net over F2, using
- t-expansion [i] based on digital (39, 93, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(42, 93, 93)-Net over F2 — Upper bound on s (digital)
There is no digital (42, 93, 94)-net over F2, because
- 7 times m-reduction [i] would yield digital (42, 86, 94)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(286, 94, F2, 44) (dual of [94, 8, 45]-code), but
- adding a parity check bit [i] would yield linear OA(287, 95, F2, 45) (dual of [95, 8, 46]-code), but
- “DHM†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(287, 95, F2, 45) (dual of [95, 8, 46]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(286, 94, F2, 44) (dual of [94, 8, 45]-code), but
(42, 93, 94)-Net in Base 2 — Upper bound on s
There is no (42, 93, 95)-net in base 2, because
- 3 times m-reduction [i] would yield (42, 90, 95)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(290, 95, S2, 48), but
- adding a parity check bit [i] would yield OA(291, 96, S2, 49), but
- the (dual) Plotkin bound shows that M ≥ 79228 162514 264337 593543 950336 / 25 > 291 [i]
- adding a parity check bit [i] would yield OA(291, 96, S2, 49), but
- extracting embedded orthogonal array [i] would yield OA(290, 95, S2, 48), but