Best Known (6, 6+35, s)-Nets in Base 7
(6, 6+35, 14)-Net over F7 — Constructive and digital
Digital (6, 41, 14)-net over F7, using
- net from sequence [i] based on digital (6, 13)-sequence over F7, using
(6, 6+35, 24)-Net over F7 — Digital
Digital (6, 41, 24)-net over F7, using
- t-expansion [i] based on digital (4, 41, 24)-net over F7, using
- net from sequence [i] based on digital (4, 23)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 4 and N(F) ≥ 24, using
- net from sequence [i] based on digital (4, 23)-sequence over F7, using
(6, 6+35, 65)-Net over F7 — Upper bound on s (digital)
There is no digital (6, 41, 66)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(741, 66, F7, 35) (dual of [66, 25, 36]-code), but
- residual code [i] would yield OA(76, 30, S7, 5), but
- 1 times truncation [i] would yield OA(75, 29, S7, 4), but
- the linear programming bound shows that M ≥ 3 384381 / 197 > 75 [i]
- 1 times truncation [i] would yield OA(75, 29, S7, 4), but
- residual code [i] would yield OA(76, 30, S7, 5), but
(6, 6+35, 76)-Net in Base 7 — Upper bound on s
There is no (6, 41, 77)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(741, 77, S7, 35), but
- the linear programming bound shows that M ≥ 1 261556 207333 721370 976650 036899 535102 800487 164084 585216 010033 036212 110407 / 25 232803 147664 626567 913594 841375 581005 > 741 [i]