Best Known (258−122, 258, s)-Nets in Base 4
(258−122, 258, 130)-Net over F4 — Constructive and digital
Digital (136, 258, 130)-net over F4, using
- t-expansion [i] based on digital (105, 258, 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
(258−122, 258, 215)-Net over F4 — Digital
Digital (136, 258, 215)-net over F4, using
(258−122, 258, 2713)-Net in Base 4 — Upper bound on s
There is no (136, 258, 2714)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 215071 114758 850636 592689 813289 273408 684627 962574 714345 076239 377875 805211 511817 570349 738417 376343 230663 408718 041894 325197 497964 306219 335814 469753 266320 210080 > 4258 [i]