Best Known (96, 96+77, s)-Nets in Base 3
(96, 96+77, 80)-Net over F3 — Constructive and digital
Digital (96, 173, 80)-net over F3, using
- 3 times m-reduction [i] based on digital (96, 176, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 88, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- trace code for nets [i] based on digital (8, 88, 40)-net over F9, using
(96, 96+77, 122)-Net over F3 — Digital
Digital (96, 173, 122)-net over F3, using
(96, 96+77, 1047)-Net in Base 3 — Upper bound on s
There is no (96, 173, 1048)-net in base 3, because
- 1 times m-reduction [i] would yield (96, 172, 1048)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 11654 086831 142847 356775 315513 171723 756586 014574 160170 524299 986362 151031 614328 422545 > 3172 [i]