Best Known (161, 161+99, s)-Nets in Base 4
(161, 161+99, 200)-Net over F4 — Constructive and digital
Digital (161, 260, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 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) = 161 and N(F) ≥ 200, using
(161, 161+99, 435)-Net over F4 — Digital
Digital (161, 260, 435)-net over F4, using
(161, 161+99, 9653)-Net in Base 4 — Upper bound on s
There is no (161, 260, 9654)-net in base 4, because
- 1 times m-reduction [i] would yield (161, 259, 9654)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 859162 702947 088170 928390 432626 168093 725122 832809 383481 014538 624256 133958 901009 252436 152604 637098 612660 656978 770221 007386 800538 057838 545065 559346 942938 444643 > 4259 [i]