Best Known (101, 101+139, s)-Nets in Base 4
(101, 101+139, 104)-Net over F4 — Constructive and digital
Digital (101, 240, 104)-net over F4, using
- t-expansion [i] based on digital (73, 240, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(101, 101+139, 144)-Net over F4 — Digital
Digital (101, 240, 144)-net over F4, using
- t-expansion [i] based on digital (91, 240, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(101, 101+139, 1020)-Net in Base 4 — Upper bound on s
There is no (101, 240, 1021)-net in base 4, because
- 1 times m-reduction [i] would yield (101, 239, 1021)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 808329 719894 377206 951180 518696 655643 677933 669024 347908 443679 431917 961452 522067 323322 305898 919438 775510 202216 515157 433566 781267 069187 618420 768596 > 4239 [i]