Best Known (2, 2+18, s)-Nets in Base 7
(2, 2+18, 10)-Net over F7 — Constructive and digital
Digital (2, 20, 10)-net over F7, using
- net from sequence [i] based on digital (2, 9)-sequence over F7, using
- Niederreiter sequence (Bratley–Fox–Niederreiter implementation) with equidistant coordinate [i]
(2, 2+18, 16)-Net over F7 — Digital
Digital (2, 20, 16)-net over F7, using
- net from sequence [i] based on digital (2, 15)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 2 and N(F) ≥ 16, using
(2, 2+18, 22)-Net over F7 — Upper bound on s (digital)
There is no digital (2, 20, 23)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(720, 23, F7, 18) (dual of [23, 3, 19]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
(2, 2+18, 32)-Net in Base 7 — Upper bound on s
There is no (2, 20, 33)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(720, 33, S7, 18), but
- the linear programming bound shows that M ≥ 418 031683 133189 273239 / 4807 > 720 [i]