Best Known (115−42, 115, s)-Nets in Base 5
(115−42, 115, 252)-Net over F5 — Constructive and digital
Digital (73, 115, 252)-net over F5, using
- 11 times m-reduction [i] based on digital (73, 126, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 63, 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, 63, 126)-net over F25, using
(115−42, 115, 364)-Net over F5 — Digital
Digital (73, 115, 364)-net over F5, using
(115−42, 115, 14577)-Net in Base 5 — Upper bound on s
There is no (73, 115, 14578)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 241 048695 514592 617185 380642 632074 391217 555371 239282 976800 491562 328464 675519 775945 > 5115 [i]