Best Known (18, 102, s)-Nets in Base 7
(18, 102, 26)-Net over F7 — Constructive and digital
Digital (18, 102, 26)-net over F7, using
- net from sequence [i] based on digital (18, 25)-sequence over F7, using
(18, 102, 51)-Net over F7 — Digital
Digital (18, 102, 51)-net over F7, using
- net from sequence [i] based on digital (18, 50)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 18 and N(F) ≥ 51, using
(18, 102, 256)-Net over F7 — Upper bound on s (digital)
There is no digital (18, 102, 257)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(7102, 257, F7, 84) (dual of [257, 155, 85]-code), but
- residual code [i] would yield OA(718, 172, S7, 12), but
- the linear programming bound shows that M ≥ 4 737429 508718 418109 748150 / 2895 922947 > 718 [i]
- residual code [i] would yield OA(718, 172, S7, 12), but
(18, 102, 283)-Net in Base 7 — Upper bound on s
There is no (18, 102, 284)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 164 491472 021703 765525 459899 330911 986970 339999 779612 092969 824656 368371 124046 190610 604265 > 7102 [i]