Best Known (135, 135+114, s)-Nets in Base 4
(135, 135+114, 130)-Net over F4 — Constructive and digital
Digital (135, 249, 130)-net over F4, using
- t-expansion [i] based on digital (105, 249, 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+114, 230)-Net over F4 — Digital
Digital (135, 249, 230)-net over F4, using
(135, 135+114, 3093)-Net in Base 4 — Upper bound on s
There is no (135, 249, 3094)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 829731 775679 134148 234724 574183 175161 657130 851321 735017 977985 004682 809872 406698 027356 771118 903216 789743 720636 120576 160464 374586 407947 217311 425420 560000 > 4249 [i]