Best Known (68, 68+70, s)-Nets in Base 4
(68, 68+70, 66)-Net over F4 — Constructive and digital
Digital (68, 138, 66)-net over F4, using
- t-expansion [i] based on digital (49, 138, 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
(68, 68+70, 100)-Net over F4 — Digital
Digital (68, 138, 100)-net over F4, using
(68, 68+70, 1068)-Net in Base 4 — Upper bound on s
There is no (68, 138, 1069)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 125184 698461 786961 342136 698807 237114 770008 193743 523486 921902 865405 758603 091682 398780 > 4138 [i]