Best Known (69, 139, s)-Nets in Base 4
(69, 139, 66)-Net over F4 — Constructive and digital
Digital (69, 139, 66)-net over F4, using
- t-expansion [i] based on digital (49, 139, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(69, 139, 103)-Net over F4 — Digital
Digital (69, 139, 103)-net over F4, using
(69, 139, 1112)-Net in Base 4 — Upper bound on s
There is no (69, 139, 1113)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 495742 182636 915624 192616 839627 597718 892751 557518 918489 418880 024011 796729 057030 290128 > 4139 [i]