Best Known (65−56, 65, s)-Nets in Base 7
(65−56, 65, 17)-Net over F7 — Constructive and digital
Digital (9, 65, 17)-net over F7, using
- net from sequence [i] based on digital (9, 16)-sequence over F7, using
(65−56, 65, 38)-Net over F7 — Digital
Digital (9, 65, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
(65−56, 65, 70)-Net over F7 — Upper bound on s (digital)
There is no digital (9, 65, 71)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(765, 71, F7, 56) (dual of [71, 6, 57]-code), but
- residual code [i] would yield linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
(65−56, 65, 72)-Net in Base 7 — Upper bound on s
There is no (9, 65, 73)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(765, 73, S7, 56), but
- the linear programming bound shows that M ≥ 22 811215 366107 453768 378823 709022 673015 989035 549897 706388 838989 / 2 012613 > 765 [i]