MinT - Best Known (220−95, 220, s)-Nets in Base 4

Best Known (220−95, 220, s)-Nets in Base 4

(220−95, 220, 130)-Net over F₄ — Constructive and digital

Digital (125, 220, 130)-net over F₄, using

t-expansion [i] based on digital (105, 220, 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]

(220−95, 220, 248)-Net over F₄ — Digital

Digital (125, 220, 248)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−95, 220, 3872)-Net in Base 4 — Upper bound on s

There is no (125, 220, 3873)-net in base 4, because

1 times m-reduction [i] would yield (125, 219, 3873)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 711669 304094 809237 576452 835817 398093 354627 123434 078889 458893 593140 328973 176534 968647 052256 511635 150335 208769 537957 199337 527849 357568 > 4²¹⁹ [i]