Best Known (105, 105+107, s)-Nets in Base 4
(105, 105+107, 130)-Net over F4 — Constructive and digital
Digital (105, 212, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second 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) = 105 and N(F) ≥ 130, using
(105, 105+107, 147)-Net over F4 — Digital
Digital (105, 212, 147)-net over F4, using
(105, 105+107, 1668)-Net in Base 4 — Upper bound on s
There is no (105, 212, 1669)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 211, 1669)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10 852117 565127 066150 856831 425950 693189 357358 911780 964447 643284 800469 290625 813654 893255 551907 783070 534727 359645 947362 611811 209760 > 4211 [i]