Best Known (126, 126+115, s)-Nets in Base 4
(126, 126+115, 130)-Net over F4 — Constructive and digital
Digital (126, 241, 130)-net over F4, using
- t-expansion [i] based on digital (105, 241, 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+115, 196)-Net over F4 — Digital
Digital (126, 241, 196)-net over F4, using
(126, 126+115, 2476)-Net in Base 4 — Upper bound on s
There is no (126, 241, 2477)-net in base 4, because
- 1 times m-reduction [i] would yield (126, 240, 2477)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3 191617 565939 483121 482048 545491 258557 914749 279618 602088 995499 008012 817097 732658 984774 728550 284930 186015 619682 946970 773203 498488 461969 192665 260800 > 4240 [i]