Best Known (29, 29+29, s)-Nets in Base 5
(29, 29+29, 52)-Net over F5 — Constructive and digital
Digital (29, 58, 52)-net over F5, using
- trace code for nets [i] based on digital (0, 29, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
(29, 29+29, 69)-Net over F5 — Digital
Digital (29, 58, 69)-net over F5, using
(29, 29+29, 1049)-Net in Base 5 — Upper bound on s
There is no (29, 58, 1050)-net in base 5, because
- 1 times m-reduction [i] would yield (29, 57, 1050)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 6958 516230 804077 744063 059206 540273 071361 > 557 [i]