Best Known (62, 62+128, s)-Nets in Base 3
(62, 62+128, 48)-Net over F3 — Constructive and digital
Digital (62, 190, 48)-net over F3, using
- t-expansion [i] based on digital (45, 190, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(62, 62+128, 64)-Net over F3 — Digital
Digital (62, 190, 64)-net over F3, using
- t-expansion [i] based on digital (49, 190, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(62, 62+128, 195)-Net over F3 — Upper bound on s (digital)
There is no digital (62, 190, 196)-net over F3, because
- 2 times m-reduction [i] would yield digital (62, 188, 196)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3188, 196, F3, 126) (dual of [196, 8, 127]-code), but
- residual code [i] would yield linear OA(362, 69, F3, 42) (dual of [69, 7, 43]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(362, 69, F3, 42) (dual of [69, 7, 43]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(3188, 196, F3, 126) (dual of [196, 8, 127]-code), but
(62, 62+128, 263)-Net in Base 3 — Upper bound on s
There is no (62, 190, 264)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 5 413759 219134 719766 592509 896797 857493 283917 997324 049344 884464 507894 859675 892385 957535 612929 > 3190 [i]