Best Known (135, 135+125, s)-Nets in Base 4
(135, 135+125, 130)-Net over F4 — Constructive and digital
Digital (135, 260, 130)-net over F4, using
- t-expansion [i] based on digital (105, 260, 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
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(135, 135+125, 205)-Net over F4 — Digital
Digital (135, 260, 205)-net over F4, using
(135, 135+125, 2560)-Net in Base 4 — Upper bound on s
There is no (135, 260, 2561)-net in base 4, because
- 1 times m-reduction [i] would yield (135, 259, 2561)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 858555 681716 943125 767595 608904 860624 682631 716366 195337 957321 286760 477762 397794 178775 336783 347872 935176 216880 860455 184521 544796 882938 792652 115389 617382 192384 > 4259 [i]