MinT - Best Known (115−57, 115, s)-Nets in Base 4

Best Known (115−57, 115, s)-Nets in Base 4

(115−57, 115, 66)-Net over F₄ — Constructive and digital

Digital (58, 115, 66)-net over F₄, using

t-expansion [i] based on digital (49, 115, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(115−57, 115, 92)-Net over F₄ — Digital

Digital (58, 115, 92)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−57, 115, 1041)-Net in Base 4 — Upper bound on s

There is no (58, 115, 1042)-net in base 4, because

1 times m-reduction [i] would yield (58, 114, 1042)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 433 522818 128193 576663 770410 128093 995018 889339 837149 148005 542733 837056 > 4¹¹⁴ [i]