Best Known (88, 123, s)-Nets in Base 3
(88, 123, 228)-Net over F3 — Constructive and digital
Digital (88, 123, 228)-net over F3, using
- trace code for nets [i] based on digital (6, 41, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
(88, 123, 356)-Net over F3 — Digital
Digital (88, 123, 356)-net over F3, using
(88, 123, 9510)-Net in Base 3 — Upper bound on s
There is no (88, 123, 9511)-net in base 3, because
- 1 times m-reduction [i] would yield (88, 122, 9511)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 16183 573486 814550 087746 889364 509615 682972 790231 226690 967599 > 3122 [i]