Best Known (62, 62+20, s)-Nets in Base 7
(62, 62+20, 688)-Net over F7 — Constructive and digital
Digital (62, 82, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 41, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(62, 62+20, 5875)-Net over F7 — Digital
Digital (62, 82, 5875)-net over F7, using
(62, 62+20, 6421382)-Net in Base 7 — Upper bound on s
There is no (62, 82, 6421383)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 1986 275021 629224 117348 087603 390841 810476 140311 131790 969360 983052 141333 > 782 [i]