Best Known (126, 126+116, s)-Nets in Base 4
(126, 126+116, 130)-Net over F4 — Constructive and digital
Digital (126, 242, 130)-net over F4, using
- t-expansion [i] based on digital (105, 242, 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
(126, 126+116, 194)-Net over F4 — Digital
Digital (126, 242, 194)-net over F4, using
(126, 126+116, 2385)-Net in Base 4 — Upper bound on s
There is no (126, 242, 2386)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 50 471715 116847 906135 971771 417675 603547 517911 410223 614379 446775 751802 013497 569083 067694 220158 393615 663119 960532 754003 061564 488664 362826 905713 024800 > 4242 [i]