Best Known (198−101, 198, s)-Nets in Base 4
(198−101, 198, 104)-Net over F4 — Constructive and digital
Digital (97, 198, 104)-net over F4, using
- t-expansion [i] based on digital (73, 198, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(198−101, 198, 144)-Net over F4 — Digital
Digital (97, 198, 144)-net over F4, using
- t-expansion [i] based on digital (91, 198, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(198−101, 198, 1489)-Net in Base 4 — Upper bound on s
There is no (97, 198, 1490)-net in base 4, because
- 1 times m-reduction [i] would yield (97, 197, 1490)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 41513 301000 628315 350620 922226 348143 060191 166482 718524 985403 020789 319498 294902 655835 992448 535465 875337 142576 669948 613776 > 4197 [i]