Best Known (232−107, 232, s)-Nets in Base 4
(232−107, 232, 130)-Net over F4 — Constructive and digital
Digital (125, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(232−107, 232, 211)-Net over F4 — Digital
Digital (125, 232, 211)-net over F4, using
(232−107, 232, 2845)-Net in Base 4 — Upper bound on s
There is no (125, 232, 2846)-net in base 4, because
- 1 times m-reduction [i] would yield (125, 231, 2846)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 007102 232183 387483 724736 105298 003475 807981 034296 567052 041013 232866 738537 542392 239114 424897 221471 134580 764839 686562 892759 437379 654592 318600 > 4231 [i]