Best Known (91, 91+136, s)-Nets in Base 4
(91, 91+136, 104)-Net over F4 — Constructive and digital
Digital (91, 227, 104)-net over F4, using
- t-expansion [i] based on digital (73, 227, 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
(91, 91+136, 144)-Net over F4 — Digital
Digital (91, 227, 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
(91, 91+136, 836)-Net in Base 4 — Upper bound on s
There is no (91, 227, 837)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 46767 618875 364963 801111 853589 542350 914466 666360 805481 714945 258981 482849 156735 806246 867407 591243 804188 380334 267962 977573 913215 007472 876885 > 4227 [i]