Best Known (53, 113, s)-Nets in Base 4
(53, 113, 66)-Net over F4 — Constructive and digital
Digital (53, 113, 66)-net over F4, using
- t-expansion [i] based on digital (49, 113, 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
(53, 113, 91)-Net over F4 — Digital
Digital (53, 113, 91)-net over F4, using
- t-expansion [i] based on digital (50, 113, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(53, 113, 719)-Net in Base 4 — Upper bound on s
There is no (53, 113, 720)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 109 794997 462497 841839 637540 144611 031831 765592 353367 124616 998655 477924 > 4113 [i]