Best Known (4, 10, s)-Nets in Base 7
(4, 10, 21)-Net over F7 — Constructive and digital
Digital (4, 10, 21)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using
- the rational function field F7(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (0, 3, 8)-net over F7, using
(4, 10, 28)-Net over F7 — Digital
Digital (4, 10, 28)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(710, 28, F7, 6) (dual of [28, 18, 7]-code), using
- a “XX†code from Brouwer’s database [i]
(4, 10, 197)-Net in Base 7 — Upper bound on s
There is no (4, 10, 198)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 285 825673 > 710 [i]
- extracting embedded orthogonal array [i] would yield OA(710, 198, S7, 6), but
- the linear programming bound shows that M ≥ 29 158533 965015 / 102491 > 710 [i]