Best Known (48, 48+79, s)-Nets in Base 3
(48, 48+79, 48)-Net over F3 — Constructive and digital
Digital (48, 127, 48)-net over F3, using
- t-expansion [i] based on digital (45, 127, 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
(48, 48+79, 56)-Net over F3 — Digital
Digital (48, 127, 56)-net over F3, using
- t-expansion [i] based on digital (40, 127, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
(48, 48+79, 231)-Net in Base 3 — Upper bound on s
There is no (48, 127, 232)-net in base 3, because
- 1 times m-reduction [i] would yield (48, 126, 232)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 414510 743298 882523 970040 093663 085346 431294 994660 338749 905377 > 3126 [i]