Best Known (238−59, 238, s)-Nets in Base 3
(238−59, 238, 328)-Net over F3 — Constructive and digital
Digital (179, 238, 328)-net over F3, using
- 32 times duplication [i] based on digital (177, 236, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 59, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 59, 82)-net over F81, using
(238−59, 238, 1014)-Net over F3 — Digital
Digital (179, 238, 1014)-net over F3, using
(238−59, 238, 46244)-Net in Base 3 — Upper bound on s
There is no (179, 238, 46245)-net in base 3, because
- 1 times m-reduction [i] would yield (179, 237, 46245)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 119665 013917 264449 530124 850791 217865 790039 601849 979702 332586 992778 496944 965696 517603 571075 587563 916775 727379 648251 > 3237 [i]