MinT - Best Known (226−111, 226, s)-Nets in Base 4

Best Known (226−111, 226, s)-Nets in Base 4

(226−111, 226, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(226−111, 226, 169)-Net over F₄ — Digital

Digital (115, 226, 169)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−111, 226, 2020)-Net in Base 4 — Upper bound on s

There is no (115, 226, 2021)-net in base 4, because

1 times m-reduction [i] would yield (115, 225, 2021)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2948 916754 842686 004987 270884 457384 413206 122820 465356 770776 076187 120855 532865 346619 143575 529077 605390 653397 017567 746022 931962 438120 258496 > 4²²⁵ [i]