Best Known (93−46, 93, s)-Nets in Base 2
(93−46, 93, 34)-Net over F2 — Constructive and digital
Digital (47, 93, 34)-net over F2, using
- t-expansion [i] based on digital (45, 93, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
(93−46, 93, 36)-Net over F2 — Digital
Digital (47, 93, 36)-net over F2, using
- net from sequence [i] based on digital (47, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 47 and N(F) ≥ 36, using
(93−46, 93, 106)-Net over F2 — Upper bound on s (digital)
There is no digital (47, 93, 107)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(293, 107, F2, 46) (dual of [107, 14, 47]-code), but
- adding a parity check bit [i] would yield linear OA(294, 108, F2, 47) (dual of [108, 14, 48]-code), but
(93−46, 93, 107)-Net in Base 2 — Upper bound on s
There is no (47, 93, 108)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(293, 108, S2, 46), but
- the linear programming bound shows that M ≥ 8 279342 982740 623278 525342 810112 / 833 > 293 [i]