Best Known (81, 81+72, s)-Nets in Base 4
(81, 81+72, 104)-Net over F4 — Constructive and digital
Digital (81, 153, 104)-net over F4, using
- t-expansion [i] based on digital (73, 153, 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
(81, 81+72, 138)-Net over F4 — Digital
Digital (81, 153, 138)-net over F4, using
(81, 81+72, 1694)-Net in Base 4 — Upper bound on s
There is no (81, 153, 1695)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 133 034733 066131 899638 989723 323215 618065 516233 103756 256789 900464 127508 620623 356915 545192 158980 > 4153 [i]