Best Known (65, 65+78, s)-Nets in Base 4
(65, 65+78, 66)-Net over F4 — Constructive and digital
Digital (65, 143, 66)-net over F4, using
- t-expansion [i] based on digital (49, 143, 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
(65, 65+78, 99)-Net over F4 — Digital
Digital (65, 143, 99)-net over F4, using
- t-expansion [i] based on digital (61, 143, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(65, 65+78, 796)-Net in Base 4 — Upper bound on s
There is no (65, 143, 797)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 129 502851 774512 337843 120195 945601 419402 433539 926472 206946 079238 508917 028966 621023 082688 > 4143 [i]