MinT - Best Known (226−109, 226, s)-Nets in Base 4

Best Known (226−109, 226, s)-Nets in Base 4

(226−109, 226, 130)-Net over F₄ — Constructive and digital

Digital (117, 226, 130)-net over F₄, using

t-expansion [i] based on digital (105, 226, 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]

(226−109, 226, 179)-Net over F₄ — Digital

Digital (117, 226, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−109, 226, 2210)-Net in Base 4 — Upper bound on s

There is no (117, 226, 2211)-net in base 4, because

1 times m-reduction [i] would yield (117, 225, 2211)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2970 892323 290197 181385 507949 292961 188779 964506 026636 729244 066728 588856 313044 347078 931471 910231 660533 530823 355445 533500 844682 056161 827040 > 4²²⁵ [i]