Best Known (115, 115+91, s)-Nets in Base 4
(115, 115+91, 130)-Net over F4 — Constructive and digital
Digital (115, 206, 130)-net over F4, using
- t-expansion [i] based on digital (105, 206, 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
(115, 115+91, 218)-Net over F4 — Digital
Digital (115, 206, 218)-net over F4, using
(115, 115+91, 3212)-Net in Base 4 — Upper bound on s
There is no (115, 206, 3213)-net in base 4, because
- 1 times m-reduction [i] would yield (115, 205, 3213)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2669 509967 560981 674667 159618 775561 316962 316845 344507 756556 489704 382118 632825 893693 761445 742852 945267 538853 668508 538772 095728 > 4205 [i]