Best Known (97, 97+86, s)-Nets in Base 2
(97, 97+86, 54)-Net over F2 — Constructive and digital
Digital (97, 183, 54)-net over F2, using
- t-expansion [i] based on digital (95, 183, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 5 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (95, 53)-sequence over F2, using
(97, 97+86, 65)-Net over F2 — Digital
Digital (97, 183, 65)-net over F2, using
- t-expansion [i] based on digital (95, 183, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(97, 97+86, 224)-Net over F2 — Upper bound on s (digital)
There is no digital (97, 183, 225)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2183, 225, F2, 86) (dual of [225, 42, 87]-code), but
- construction Y1 [i] would yield
- linear OA(2182, 211, F2, 86) (dual of [211, 29, 87]-code), but
- adding a parity check bit [i] would yield linear OA(2183, 212, F2, 87) (dual of [212, 29, 88]-code), but
- OA(242, 225, S2, 14), but
- discarding factors would yield OA(242, 219, S2, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 498367 189624 > 242 [i]
- discarding factors would yield OA(242, 219, S2, 14), but
- linear OA(2182, 211, F2, 86) (dual of [211, 29, 87]-code), but
- construction Y1 [i] would yield
(97, 97+86, 263)-Net in Base 2 — Upper bound on s
There is no (97, 183, 264)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 12 609114 669394 245230 552698 575785 673569 515084 089643 101728 > 2183 [i]