Best Known (105, 105+93, s)-Nets in Base 4
(105, 105+93, 130)-Net over F4 — Constructive and digital
Digital (105, 198, 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+93, 173)-Net over F4 — Digital
Digital (105, 198, 173)-net over F4, using
(105, 105+93, 2234)-Net in Base 4 — Upper bound on s
There is no (105, 198, 2235)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 197, 2235)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 40459 071673 905183 808134 415410 371496 179898 670985 346492 424976 784940 271826 256298 156549 848896 915527 716688 574858 972667 825324 > 4197 [i]