Best Known (209−114, 209, s)-Nets in Base 4
(209−114, 209, 104)-Net over F4 — Constructive and digital
Digital (95, 209, 104)-net over F4, using
- t-expansion [i] based on digital (73, 209, 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
(209−114, 209, 144)-Net over F4 — Digital
Digital (95, 209, 144)-net over F4, using
- t-expansion [i] based on digital (91, 209, 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
(209−114, 209, 1140)-Net in Base 4 — Upper bound on s
There is no (95, 209, 1141)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 688946 365303 913685 113411 053490 159587 791233 106561 641643 124023 565492 215898 362455 051282 458966 100234 097379 518540 615681 282960 668608 > 4209 [i]