Best Known (137, 137+122, s)-Nets in Base 4
(137, 137+122, 130)-Net over F4 — Constructive and digital
Digital (137, 259, 130)-net over F4, using
- t-expansion [i] based on digital (105, 259, 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
(137, 137+122, 218)-Net over F4 — Digital
Digital (137, 259, 218)-net over F4, using
(137, 137+122, 2777)-Net in Base 4 — Upper bound on s
There is no (137, 259, 2778)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 869122 990613 405886 315147 393708 983090 791849 069375 419756 104354 972943 975746 668057 447537 567926 255310 924260 973310 817024 380698 647535 536058 517749 304462 043318 331600 > 4259 [i]