Best Known (206−101, 206, s)-Nets in Base 4
(206−101, 206, 130)-Net over F4 — Constructive and digital
Digital (105, 206, 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
(206−101, 206, 157)-Net over F4 — Digital
Digital (105, 206, 157)-net over F4, using
(206−101, 206, 1868)-Net in Base 4 — Upper bound on s
There is no (105, 206, 1869)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 205, 1869)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2646 881266 765789 705476 573258 841960 021267 928441 913723 525194 160203 023469 085265 272135 289447 524123 021948 520644 432153 555568 496296 > 4205 [i]