Best Known (191−94, 191, s)-Nets in Base 2
(191−94, 191, 54)-Net over F2 — Constructive and digital
Digital (97, 191, 54)-net over F2, using
- t-expansion [i] based on digital (95, 191, 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
(191−94, 191, 65)-Net over F2 — Digital
Digital (97, 191, 65)-net over F2, using
- t-expansion [i] based on digital (95, 191, 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
(191−94, 191, 213)-Net over F2 — Upper bound on s (digital)
There is no digital (97, 191, 214)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2191, 214, F2, 94) (dual of [214, 23, 95]-code), but
- residual code [i] would yield OA(297, 119, S2, 47), but
- 1 times truncation [i] would yield OA(296, 118, S2, 46), but
- the linear programming bound shows that M ≥ 3649 328393 569529 653896 227896 426496 / 35409 > 296 [i]
- 1 times truncation [i] would yield OA(296, 118, S2, 46), but
- residual code [i] would yield OA(297, 119, S2, 47), but
(191−94, 191, 243)-Net in Base 2 — Upper bound on s
There is no (97, 191, 244)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3286 345835 685558 350605 490942 186974 822130 251388 005033 010828 > 2191 [i]