Best Known (254−117, 254, s)-Nets in Base 4
(254−117, 254, 130)-Net over F4 — Constructive and digital
Digital (137, 254, 130)-net over F4, using
- t-expansion [i] based on digital (105, 254, 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
(254−117, 254, 230)-Net over F4 — Digital
Digital (137, 254, 230)-net over F4, using
(254−117, 254, 3117)-Net in Base 4 — Upper bound on s
There is no (137, 254, 3118)-net in base 4, because
- 1 times m-reduction [i] would yield (137, 253, 3118)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 212 807520 550956 865371 160110 228422 632885 338742 368228 025387 022219 821243 299618 907698 691747 226924 361340 114276 266308 009240 504175 436743 475517 481169 611214 691200 > 4253 [i]