Best Known (29−14, 29, s)-Nets in Base 2
(29−14, 29, 17)-Net over F2 — Constructive and digital
Digital (15, 29, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(29−14, 29, 41)-Net over F2 — Upper bound on s (digital)
There is no digital (15, 29, 42)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(229, 42, F2, 14) (dual of [42, 13, 15]-code), but
- adding a parity check bit [i] would yield linear OA(230, 43, F2, 15) (dual of [43, 13, 16]-code), but
(29−14, 29, 50)-Net in Base 2 — Upper bound on s
There is no (15, 29, 51)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 576 635768 > 229 [i]