MinT - Best Known (229−103, 229, s)-Nets in Base 4

Best Known (229−103, 229, s)-Nets in Base 4

(229−103, 229, 130)-Net over F₄ — Constructive and digital

Digital (126, 229, 130)-net over F₄, using

t-expansion [i] based on digital (105, 229, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(229−103, 229, 226)-Net over F₄ — Digital

Digital (126, 229, 226)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−103, 229, 3211)-Net in Base 4 — Upper bound on s

There is no (126, 229, 3212)-net in base 4, because

1 times m-reduction [i] would yield (126, 228, 3212)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 188118 549176 803864 582428 162402 443006 476359 574250 147207 345853 299872 632293 142730 404123 458549 357951 868990 491193 990562 118852 236929 816177 586600 > 4²²⁸ [i]