Best Known (170−65, 170, s)-Nets in Base 4
(170−65, 170, 130)-Net over F4 — Constructive and digital
Digital (105, 170, 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
(170−65, 170, 296)-Net over F4 — Digital
Digital (105, 170, 296)-net over F4, using
(170−65, 170, 6421)-Net in Base 4 — Upper bound on s
There is no (105, 170, 6422)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 169, 6422)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 561798 788889 186270 294397 375482 577041 431726 796205 495940 183218 622550 494490 786147 591804 373694 739508 202920 > 4169 [i]