Best Known (48, 65, s)-Nets in Base 5
(48, 65, 268)-Net over F5 — Constructive and digital
Digital (48, 65, 268)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 16)-net over F5, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- digital (37, 54, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 27, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 27, 126)-net over F25, using
- digital (3, 11, 16)-net over F5, using
(48, 65, 1532)-Net over F5 — Digital
Digital (48, 65, 1532)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(565, 1532, F5, 17) (dual of [1532, 1467, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(565, 1562, F5, 17) (dual of [1562, 1497, 18]-code), using
(48, 65, 367606)-Net in Base 5 — Upper bound on s
There is no (48, 65, 367607)-net in base 5, because
- 1 times m-reduction [i] would yield (48, 64, 367607)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 542 102699 355190 689022 884885 252449 785811 360225 > 564 [i]