MinT - Best Known (235−111, 235, s)-Nets in Base 4

Best Known (235−111, 235, s)-Nets in Base 4

(235−111, 235, 130)-Net over F₄ — Constructive and digital

Digital (124, 235, 130)-net over F₄, using

t-expansion [i] based on digital (105, 235, 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]

(235−111, 235, 198)-Net over F₄ — Digital

Digital (124, 235, 198)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−111, 235, 2546)-Net in Base 4 — Upper bound on s

There is no (124, 235, 2547)-net in base 4, because

1 times m-reduction [i] would yield (124, 234, 2547)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 773 066236 293253 117111 315056 761239 381955 292131 879791 593044 533271 941157 865408 331795 670670 440308 933292 751146 095009 281719 995641 584917 537212 250240 > 4²³⁴ [i]