Best Known (112, 112+42, s)-Nets in Base 3
(112, 112+42, 264)-Net over F3 — Constructive and digital
Digital (112, 154, 264)-net over F3, using
- 31 times duplication [i] based on digital (111, 153, 264)-net over F3, using
- trace code for nets [i] based on digital (9, 51, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- trace code for nets [i] based on digital (9, 51, 88)-net over F27, using
(112, 112+42, 494)-Net over F3 — Digital
Digital (112, 154, 494)-net over F3, using
(112, 112+42, 13667)-Net in Base 3 — Upper bound on s
There is no (112, 154, 13668)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29 974400 952055 820225 147766 441884 612585 742528 626508 604395 794364 096411 556521 > 3154 [i]